From 1178790aad36318007e56769745f78385a3615ce Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 15 Apr 2026 17:52:33 +0200 Subject: [PATCH 01/29] add joss --- .github/workflows/JOSS.yml | 35 + joss/paper.bib | 578 +++++ joss/paper.md | 204 ++ joss/plot.svg | 4354 ++++++++++++++++++++++++++++++++++++ 4 files changed, 5171 insertions(+) create mode 100644 .github/workflows/JOSS.yml create mode 100644 joss/paper.bib create mode 100644 joss/paper.md create mode 100644 joss/plot.svg diff --git a/.github/workflows/JOSS.yml b/.github/workflows/JOSS.yml new file mode 100644 index 00000000..a94de1a6 --- /dev/null +++ b/.github/workflows/JOSS.yml @@ -0,0 +1,35 @@ +name: Compile JOSS paper + +on: + push: + paths: + - 'joss' # Se déclenche uniquement pour les changements dans le dossier paper + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v4 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + # This should be the path to the paper within your repo. + paper-path: joss/paper.md + - name: Upload PDF + uses: actions/upload-artifact@v4 + with: + name: paper + path: joss/paper.pdf + + - name: Commit PDF + uses: EndBug/add-and-commit@v9 + with: + add: 'joss/paper.pdf' + message: 'chore: update paper.pdf' + author_name: 'GitHub Actions' + author_email: 'actions@github.com' + committer_name: 'GitHub Actions' + committer_email: 'actions@github.com' \ No newline at end of file diff --git a/joss/paper.bib b/joss/paper.bib new file mode 100644 index 00000000..89f16990 --- /dev/null +++ b/joss/paper.bib @@ -0,0 +1,578 @@ + +@article{rackauckas2017differentialequations, + title={Differentialequations.jl--a performant and feature-rich ecosystem for solving differential equations in julia}, + author={Rackauckas, Christopher and Nie, Qing}, + journal={Journal of Open Research Software}, + volume={5}, + number={1}, + pages={15}, + year={2017}, + publisher={Ubiquity Press} +} + +@article{Lubin2023, + author = {Lubin, Miles and Dowson, Oscar and {Dias Garcia}, Joaquim and Huchette, Joey and Legat, Beno{\^i}t and Vielma, Juan Pablo}, + title = {{JuMP} 1.0: {R}ecent improvements to a modeling language for mathematical optimization}, + journal = {Mathematical Programming Computation}, + year = {2023}, + doi = {10.1007/s12532-023-00239-3} +} + +@software{ADNLPModels_jl, +author = {Migot, Tangi and Montoison, Alexis and Orban, Dominique and Soares Siqueira, Abel and contributors}, +license = {MPL-2.0}, +title = {{ADNLPModels.jl: Automatic Differentiation models implementing the NLPModels API}}, +url = {https://github.com/JuliaSmoothOptimizers/ADNLPModels.jl}, +year = {2023} +} + +@inproceedings{ferede2025icra, + title={One Net to Rule Them All: Domain Randomization in Quadcopter Racing Across Different Platforms}, + author={Ferede, Robin and Blaha, Till and Lucassen, Erin and De Wagter, Christophe and de Croon, Guido C. H. E.}, + booktitle={2025 IEEE International Conference on Robotics and Automation (ICRA)}, + pages={6357--6363}, + year={2025}, + doi={10.1109/ICRA55743.2025.11128790} +} + +@unpublished{bouali:hal-04928858, + TITLE = {{Regularization of optimal control problems on stratified domains using additional controls}}, + AUTHOR = {Bouali, Anas and Rapaport, Alain and Bayen, T{\'e}rence}, + URL = {https://hal.inrae.fr/hal-04928858}, + NOTE = {working paper or preprint}, + HAL_LOCAL_REFERENCE = {MISTEA - Axe syst{\`e}mes dynamiques}, + YEAR = {2025}, + MONTH = Feb, + KEYWORDS = {optimal control ; Filippov solutions ; discontinuous dynamics ; regularization ; penalty method ; direct method}, + PDF = {https://hal.inrae.fr/hal-04928858v2/file/BRB.pdf}, + HAL_ID = {hal-04928858}, + HAL_VERSION = {v2} +} + +@article{bliman:hal-05194927, + title = {{On the problem of minimizing the epidemic final size for SIR model by social distancing}}, + author = {Bliman, Pierre-Alexandre and Bouali, Anas and Loisel, Patrice and Rapaport, Alain and Virelizier, Arnaud}, + journal = {Mathematical Biosciences and Engineering}, + volume = {23}, + number = {3}, + pages = {567--593}, + year = {2026}, + doi = {10.3934/mbe.2026022}, +} + +@software{OptimalControl_jl, + author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre and Sed, Sophia}, + doi = {10.5281/zenodo.13336563}, + license = {MIT}, + title = {{OptimalControl.jl: a Julia package to model and solve optimal control problems with ODEs}}, + url = {https://control-toolbox.org/OptimalControl.jl}, + year = {2024} +} + +@software{OptimalControlProblems_jl, + author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre}, + doi = {10.5281/zenodo.17013180}, + license = {MIT}, + title = {{OptimalControlProblems.jl: a collection of optimal control problems with ODEs in Julia}}, + url = {https://control-toolbox.org/OptimalControlProblems.jl}, + year = {2024} +} + +@article{Bezanson2017, + title={Julia: A fresh approach to numerical computing}, + author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B}, + journal={SIAM Review}, + volume={59}, + number={1}, + pages={65--98}, + year={2017}, + publisher={SIAM}, + doi={10.1137/141000671} +} + +@article{SHIN2021693, +title = {Graph-Based Modeling and Decomposition of Energy Infrastructures}, +journal = {IFAC-PapersOnLine}, +volume = {54}, +number = {3}, +pages = {693-698}, +year = {2021}, +note = {16th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2021}, +issn = {2405-8963}, +doi = {10.1016/j.ifacol.2021.08.322}, +url = {https://www.sciencedirect.com/science/article/pii/S240589632101096X}, +author = {Shin, Sungho and Coffrin, Carleton and Sundar, Kaarthik and Zavala, Victor M.}, +keywords = {Nonlinear Optimization, Decomposition, Graphs, Energy Systems}, +} + +@article{SHIN2024110651, +title = {Accelerating optimal power flow with GPUs: SIMD abstraction of nonlinear programs and condensed-space interior-point methods}, +journal = {Electric Power Systems Research}, +volume = {236}, +pages = {110651}, +year = {2024}, +issn = {0378-7796}, +doi = {10.1016/j.epsr.2024.110651}, +url = {https://www.sciencedirect.com/science/article/pii/S0378779624005376}, +author = {Shin, Sungho and Anitescu, Mihai and Pacaud, François}, +keywords = {Nonlinear programming, Automatic differentiation, GPU computing, Optimal power flow}, +} + +@article{Wachter2006, + title={On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming}, + author={W{\"a}chter, Andreas and Biegler, Lorenz T}, + journal={Mathematical Programming}, + volume={106}, + number={1}, + pages={25--57}, + year={2006}, + publisher={Springer}, + doi={10.1007/s10107-004-0559-y} +} + +@article{Patterson2014, + title={GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming}, + author={Patterson, Michael A and Rao, Anil V}, + journal={ACM Transactions on Mathematical Software}, + volume={41}, + number={1}, + pages={1--37}, + year={2014}, + publisher={ACM}, + doi={10.1145/2558904} +} + +@article{Bonnans2017, + title={The Bocop and BocHop optimization toolboxes}, + author={Bonnans, J Fr{\'e}d{\'e}ric and Martinon, Pierre and Giorgi, Daphne and Gr{\'e}lard, Vincent and Maindrault, S{\'e}bastien and Tissot, Olivier}, + journal={IFAC-PapersOnLine}, + volume={50}, + number={1}, + pages={8849--8854}, + year={2017}, + publisher={Elsevier}, + doi={10.1016/j.ifacol.2017.08.1745} +} + +@article{Houska2011, + title={ACADO toolkit—An open-source framework for automatic control and dynamic optimization}, + author={Houska, Boris and Ferreau, Hans Joachim and Diehl, Moritz}, + journal={Optimal Control Applications and Methods}, + volume={32}, + number={3}, + pages={298--312}, + year={2011}, + publisher={Wiley Online Library}, + doi={10.1002/oca.939} +} + +@article{Andersson2019, + title={CasADi: a software framework for nonlinear optimization and optimal control}, + author={Andersson, Joel AE and Gillis, Joris and Horn, Greg and Rawlings, James B and Diehl, Moritz}, + journal={Mathematical Programming Computation}, + volume={11}, + number={1}, + pages={1--36}, + year={2019}, + publisher={Springer}, + doi={10.1007/s12532-018-0139-4} +} + +@article{bonnard2007second, + title={Second order optimality conditions in the smooth case and applications in optimal control}, + author={Bonnard, Bernard and Caillau, Jean-Baptiste and Tr{\'e}lat, Emmanuel}, + journal={ESAIM: Control, Optimisation and Calculus of Variations}, + volume={13}, + number={2}, + pages={207--236}, + year={2007}, + publisher={EDP Sciences}, + doi={10.1051/cocv:2007012} +} + +@article{pulsipher2022unifying, + title = {A unifying modeling abstraction for infinite-dimensional optimization}, + journal = {Computers & Chemical Engineering}, + volume = {156}, + year = {2022}, + issn = {0098-1354}, + doi = {10.1016/j.compchemeng.2021.107567}, + url = {https://www.sciencedirect.com/science/article/pii/S0098135421003458}, + author = {Pulsipher, Joshua L. and Zhang, Weiqi and Hongisto, Tyler J. and Zavala, Victor M.} +} + +@article{caillau2012differential, + title={Differential continuation for regular optimal control problems}, + author={Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph}, + journal={Optimization Methods and Software}, + volume={27}, + number={2}, + pages={177--196}, + year={2012}, + publisher={Taylor \& Francis}, + doi={10.1080/10556788.2011.593625} +} + +@inproceedings{beschastnyi2025pulse, + title={Pulse control of affine systems with applications to quantum control}, + author={Beschastnyi, I. and Dell'Elce, L. and Pomet, J.-B. and Sacchelli, L. and Tinoco, D.}, + booktitle={2025 IEEE 64th Conference on Decision and Control (CDC)}, + pages={3769--3774}, + year={2025}, + doi={10.1109/CDC57313.2025.11312971} +} + +@unpublished{lutz:hal-05047678, + title={Minimal Time Control of Underdamped Parametric Oscillators}, + author={Lutz, Killian and Privat, Yannick}, + note={working paper or preprint}, + year={2025}, + month={Apr}, + url={https://hal.science/hal-05047678}, + hal_id={hal-05047678}, + hal_version={v3} +} + +@inproceedings{caio2025application, + title={Application of Indirect Methods to Optimal Control Problems in Epidemiology}, + author={Caio, Pedro and Silva, Cristiana J.}, + booktitle={CONTROLO 2024}, + pages={444--454}, + year={2025}, + publisher={Springer Nature Switzerland}, + address={Cham}, + doi={10.1007/978-3-031-81724-3_40} +} + +@article{opmeer2025optimal, + title={Optimal harvesting of a continuously age-structured population with density dependence}, + author={Opmeer, Mark}, + journal={PLOS ONE}, + volume={20}, + number={9}, + pages={1--12}, + year={2025}, + publisher={Public Library of Science}, + doi={10.1371/journal.pone.0333087} +} + +@inproceedings{herasimenka2026lowthrust, + title={Low-thrust trajectory optimization for the Moon-enabled Sun occultation mission concept}, + author={Herasimenka, Alesia and Baresi, Nicola and Green, Lucie and Morgan, Huw and Underwood, Craig Ian and Bridges, Chris and Jason, Susan and Lucca Fabris, Andrea and Ryden, Keith}, + booktitle={AIAA SCITECH 2026 Forum}, + year={2026}, + publisher={American Institute of Aeronautics and Astronautics (AIAA)} +} + +@article{bonnard2026zermelo, + title={The Zermelo navigation problem on the 2-sphere of revolution: an optimal control perspective with applications to micromagnetism}, + author={Bonnard, Bernard and Cots, Olivier and Privat, Yannick}, + journal={Nonlinearity}, + volume={39}, + number={1}, + pages={015006}, + year={2026}, + publisher={IOP Publishing}, + doi={10.1088/1361-6544/ae2cd9} +} + +@article{bayen2026minimum, + title={Minimum time problem for the double integrator with a loss-of-control region}, + author={Bayen, T{\'e}rence and Bouali, Anas and Bourdin, Lo{\"i}c}, + journal={Nonlinear Analysis: Hybrid Systems}, + volume={60}, + pages={101681}, + year={2026}, + doi={10.1016/j.nahs.2026.101681} +} + +@article{morsky2025vaccination, + title={Vaccination and Collective Action Under Social Norms}, + author={Morsky, Bryce}, + journal={Bulletin of Mathematical Biology}, + volume={87}, + number={5}, + pages={55}, + year={2025}, + doi={10.1007/s11538-025-01436-y} +} + +@article{evangelakos2025fast, + title={Fast protocols for charging a three-spin-chain quantum battery}, + author={Evangelakos, Vasileios and Paspalakis, Emmanuel and Stefanatos, Dionisis}, + journal={Scientific Reports}, + volume={15}, + number={1}, + pages={45626}, + year={2025}, + doi={10.1038/s41598-025-30354-1} +} + +@article{CAILLAU202213, + title = {ct: control toolbox -- Numerical tools and examples in optimal control}, + journal = {IFAC-PapersOnLine}, + volume = {55}, + number = {16}, + pages = {13--18}, + year = {2022}, + note = {18th IFAC Workshop on Control Applications of Optimization CAO 2022}, + issn = {2405-8963}, + doi = {10.1016/j.ifacol.2022.08.074}, + url = {https://www.sciencedirect.com/science/article/pii/S2405896322011648}, + author = {Caillau, Jean-Baptiste and Cots, Olivier and Martinon, Pierre}, +} + +@unpublished{innerarityimizcoz:hal-05369609, + title = {{Optimal allocation control in microbial growth under a heat-shock}}, + author = {Innerarity Imizcoz, Javier and Yabo, Agust{\'i}n G. and Djema, Walid and Francis, Francis and Gouz{\'e}, Jean-Luc}, + note = {submitted to ECC 2026}, + year = {2025}, + url = {https://inria.hal.science/hal-05369609}, + hal_id = {hal-05369609}, +} + +@article{Verschueren2021, + title = {acados -- a modular open-source framework for fast embedded optimal control}, + author = {Verschueren, Robin and Frison, Gianluca and Kouzoupis, Dimitris and Frey, Jonathan and van Duijkeren, Niels and Zanelli, Andrea and Novoselnik, Branimir and Albin, Thivaharan and Quirynen, Rien and Diehl, Moritz}, + journal = {Mathematical Programming Computation}, + year = {2021}, + doi = {10.1007/s12532-021-00208-8}, +} + +@article{arnstrom2022daqp, + author = {Arnstr{\"o}m, Daniel and Bemporad, Alberto and Axehill, Daniel}, + journal = {IEEE Transactions on Automatic Control}, + title = {A Dual Active-Set Solver for Embedded Quadratic Programming Using Recursive {LDL}$^{T}$ Updates}, + year = {2022}, + volume = {67}, + number = {8}, + pages = {4362--4369}, + doi = {10.1109/TAC.2022.3176430}, +} + +@misc{Gagnon_ModelPredictiveControl_jl_advanced_process_2024, + author = {Gagnon, Francis and Thivierge, Alex and Desbiens, Andr{\'e} and Bagge Carlson, Fredrik}, + title = {{ModelPredictiveControl.jl: advanced process control made easy in Julia}}, + year = {2024}, + doi = {10.48550/arXiv.2411.09764}, + url = {https://arxiv.org/abs/2411.09764}, +} + +@article{Falck2021, + author = {Falck, Robert D. and Gray, Justin S. and Ponnapalli, Kaushik and Wright, Ted}, + title = {dymos: A Python package for optimal control of multidisciplinary systems}, + journal = {Journal of Open Source Software}, + volume = {6}, + number = {59}, + pages = {2809}, + year = {2021}, + doi = {10.21105/joss.02809}, +} + +@article{Nicholson2018, + author = {Nicholson, Bethany and Siirola, John D. and Watson, Jean-Paul and Zavala, Victor M. and Biegler, Lorenz T.}, + title = {pyomo.dae: a modeling and automatic discretization framework for optimization with differential and algebraic equations}, + journal = {Mathematical Programming Computation}, + volume = {10}, + number = {2}, + pages = {187--223}, + year = {2018}, + doi = {10.1007/s12532-017-0127-0}, +} + +@article{Fiedler2023, + author = {Fiedler, Felix and Karg, Benjamin and L{\"u}ken, Lukas and Brandner, Dean and Heinlein, Moritz and Brabender, Felix and Lucia, Sergio}, + title = {do-mpc: Towards {FAIR} nonlinear and robust model predictive control}, + journal = {Control Engineering Practice}, + volume = {140}, + pages = {105676}, + year = {2023}, + doi = {10.1016/j.conengprac.2023.105676}, +} + +@article{Beal2018, + author = {Beal, Logan D. R. and Hill, Daniel C. and Martin, R. Abraham and Hedengren, John D.}, + title = {{GEKKO} Optimization Suite}, + journal = {Processes}, + volume = {6}, + number = {8}, + pages = {106}, + year = {2018}, + doi = {10.3390/pr6080106}, +} + +% Created references + +@software{MLStyle_jl, + author = {Thautwarm and contributors}, + title = {{MLStyle.jl: Functional programming and pattern matching for Julia}}, + url = {https://thautwarm.github.io/MLStyle.jl}, + year = {2023}, + note = {Julia package} +} + +@misc{RevelsLubinPapamarkou2016, + title = {Forward-Mode Automatic Differentiation in {J}ulia}, + author = {{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.}, + year = {2016}, + eprint = {1607.07892}, + archivePrefix = {arXiv}, + primaryClass = {cs.MS}, + url = {https://arxiv.org/abs/1607.07892} +} + +@article{dalle2026commoninterfaceautomaticdifferentiation, + author = {Guillaume Dalle and Adrian Hill}, + title = {A Common Interface for Automatic Differentiation}, + journal = {Journal of Machine Learning Research}, + year = {2026}, + volume = {27}, + number = {25}, + pages = {1--13}, + url = {http://jmlr.org/papers/v27/25-1024.html} +} + +@article{PlotsJL, + doi = {10.5334/jors.431}, + url = {https://openresearchsoftware.metajnl.com/articles/10.5334/jors.431/}, + author = {Christ, Simon and Schwabeneder, Daniel and Rackauckas, Christopher and Borregaard, Michael Krabbe and Breloff, Thomas}, + title = {Plots.jl -- a user extendable plotting API for the julia programming language}, + publisher = {Journal of Open Research Software}, + year = {2023} +} + +@article{pal2024nonlinearsolve, + author = {Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Utkarsh and Sch\"{a}fer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris}, + title = {NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia}, + year = {2025}, + publisher = {Association for Computing Machinery}, + address = {New York, NY, USA}, + issn = {0098-3500}, + doi = {10.1145/3779117}, + abstract = {Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl – a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for static array kernels for improved GPU computation on smaller problems, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as PETSc SNES, Sundials KINSOL, and MINPACK, NonlinearSolve.jl demonstrates robustness and efficiency, achieving significant advancements in solving nonlinear equations while being implemented in a high-level programming language. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.}, + note = {Just Accepted}, + journal = {ACM Trans. Math. Softw.}, + month = dec, + keywords = {Nonlinear Systems, Root Finding, Sparsity Detection, Automatic Differentiation, JuliaLang} +} + +@software{Orban_NLPModelsIpopt_jl, + author = {Orban, Dominique and Soares Siqueira, Abel and contributors}, + license = {MPL-2.0}, + month = mar, + title = {{NLPModelsIpopt.jl: A thin IPOPT wrapper for NLPModels}}, + url = {https://github.com/JuliaSmoothOptimizers/NLPModelsIpopt.jl}, + version = {0.10.1}, + year = {2023} +} + +@software{QuantumControl_jl, + author = {Machnes, Shai and Goerz, Michael H. and contributors}, + title = {{QuantumControl.jl: A framework for quantum optimal control}}, + url = {https://juliaquantumcontrol.github.io/QuantumControl.jl}, + year = {2025}, + note = {Julia package} +} + +@misc{lópezpedrares2026competitivetumorgrowthmodeling, + title={Competitive tumor growth modeling and optimal radiotherapy control via logistic equations}, + author={Javier López-Pedrares and Alba López-Rivas and Raquel Romero-Lorenzo and Jacobo Guiu-Souto and Alberto P. Muñuzuri}, + year={2026}, + eprint={2603.03901}, + archivePrefix={arXiv}, + primaryClass={math.DS}, + url={https://arxiv.org/abs/2603.03901}, +} + +@Inbook{Byrd2006, + author="Byrd, Richard H. and Nocedal, Jorge and Waltz, Richard A.", + editor="Di Pillo, G. and Roma, M.", + title="Knitro: An Integrated Package for Nonlinear Optimization", + bookTitle="Large-Scale Nonlinear Optimization", + year="2006", + publisher="Springer US", + address="Boston, MA", + pages="35--59", + isbn="978-0-387-30065-8", + doi="10.1007/0-387-30065-1_4" +} + +@misc{shin2023accelerating, + title={Accelerating Optimal Power Flow with {GPU}s: {SIMD} Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods}, + author={Sungho Shin and Fran{\c{c}}ois Pacaud and Mihai Anitescu}, + year={2023}, + eprint={2307.16830}, + archivePrefix={arXiv}, + primaryClass={math.OC} +} + +@software{Montoison_MUMPS_jl, + author = {Montoison, Alexis and Orban, Dominique and Sweeney, William R. and contributors}, + license = {MPL-2.0}, + month = feb, + title = {{MUMPS.jl: A Julia Interface to MUMPS}}, + url = {https://github.com/JuliaSmoothOptimizers/MUMPS.jl}, + version = {1.4.1}, + year = {2024} +} + +@article{MUMPS:1, + title = {A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling}, + author = {P.R. Amestoy and I. S. Duff and J. Koster and J.-Y. L'Excellent}, + journal = {SIAM Journal on Matrix Analysis and Applications}, + volume = {23}, + number = {1}, + year = {2001}, + pages = {15--41} +} + +@article{MUMPS:2, + title = {{Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures}}, + author = {P.R. Amestoy and A. Buttari and J.-Y. L'Excellent and T. Mary}, + journal = {ACM Transactions on Mathematical Software}, + volume = {45}, + number = {1}, + pages = {2:1--2:26}, + year = {2019}, + doi = {10.1145/3242094} +} + +@misc{CUDSS_nvidia, + title = {{NVIDIA cuDSS (Preview): A high-performance CUDA Library for Direct Sparse Solvers}}, + author = {{NVIDIA Corporation}}, + howpublished = {\url{https://docs.nvidia.com/cuda/cudss/index.html}}, + note = {Documentation}, + year={2025} +} + +@misc{veltz:hal-02902346, + title = {{BifurcationKit.jl}}, + author = {Veltz, Romain}, + url = {https://hal.archives-ouvertes.fr/hal-02902346}, + institution = {{Inria Sophia-Antipolis}}, + year = {2020}, + month = Jul, + keywords = {pseudo-arclength-continuation ; periodic-orbits ; floquet ; gpu ; bifurcation-diagram ; deflation ; newton-krylov}, + pdf = {https://hal.archives-ouvertes.fr/hal-02902346/file/354c9fb0d148262405609eed2cb7927818706f1f.tar.gz}, + hal_id = {hal-02902346}, + hal_version = {v1}, + eprint = {hal-02902346}, + eprinttype = {hal}, +} + +@article{Nurkanovic2022, + title={nosnoc: A software package for numerical optimal control of nonsmooth systems}, + author={Nurkanovi{\'c}, Armin and Diehl, Moritz}, + journal={IEEE Control Systems Letters}, + volume={6}, + pages={3110--3115}, + year={2022}, + publisher={IEEE} +} + +@unpublished{VanaretLeyffer2026, + author = {Vanaret, Charlie and Leyffer, Sven}, + title = {Implementing a unified solver for nonlinearly constrained optimization}, + year = {2026}, + note = {Accepted to Mathematical Programming Computation on Feb 22, 2026} +} \ No newline at end of file diff --git a/joss/paper.md b/joss/paper.md new file mode 100644 index 00000000..913604b8 --- /dev/null +++ b/joss/paper.md @@ -0,0 +1,204 @@ +--- +title: 'OptimalControl.jl: A Julia package for modeling and solving optimal control problems with ODEs' +tags: + - Julia + - optimal control + - ordinary differential equations + - direct methods + - indirect methods + - scientific computing + - mathematical optimization +authors: + - name: Jean-Baptiste Caillau + orcid: 0000-0002-1719-2016 + affiliation: "1" + - name: Olivier Cots + orcid: 0000-0002-4703-4369 + affiliation: "2" + corresponding: true + - name: Joseph Gergaud + orcid: 0009-0005-9825-8652 + affiliation: "2" + - name: Pierre Martinon + orcid: 0000-0003-0571-2376 + affiliation: "3" + - name: Sophia Sed + affiliation: "4" + +affiliations: + - name: "Université Côte d'Azur, CNRS, Inria, LJAD, France" + index: 1 + - name: "Université Toulouse, CNRS, ENSEEIHT-IRIT, France" + index: 2 + - name: "CAGE team, Inria Paris, France" + index: 3 + - name: "Inria Sophia Antipolis Méditerranée, France" + index: 4 + +date: 12 April 2026 +bibliography: paper.bib +archive_doi: 10.5281/zenodo.13336563 +--- + +# Summary + +[OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) [@OptimalControl_jl] is a Julia [@Bezanson2017] package for modeling and solving optimal control problems governed by ordinary differential equations (ODEs). As the core of the [control-toolbox ecosystem](https://control-toolbox.org), it provides a unified framework that supports both direct and indirect solution methods with applications spanning aerospace, medical imaging, epidemiology, and quantum control. + +The package features an expressive domain-specific language (DSL) built around the `@def` macro, enabling users to define control problems using notation that closely resembles standard mathematical formulations. Problems are solved through direct transcription, converting the continuous problem into a nonlinear program (NLP) using discretization schemes including Euler, trapezoidal, midpoint, and high-order Gauss-Legendre collocation. Alternatively, indirect shooting methods based on Pontryagin's Maximum Principle can be employed. The architecture relies on a modeler-solver separation that provides a modular and extensible foundation, enabling seamless execution on both CPU and GPU with minimal user intervention. + +The ecosystem includes extensive [tutorial resources](https://control-toolbox.org/Tutorials.jl), a benchmark problem collection ([OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) [@OptimalControlProblems_jl] with formulations in OptimalControl DSL and [JuMP](https://jump.dev/JuMP.jl) [@Lubin2023]), and performance comparison tools ([CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl)). Integration with Julia's ecosystem enables access to state-of-the-art tools: NLP solvers [IPOPT](https://coin-or.github.io/Ipopt) [@Wachter2006] and [MadNLP.jl](https://github.com/MadNLP/MadNLP.jl) [@SHIN2024110651; @SHIN2021693], automatic differentiation and NLP modeling through JuliaSmoothOptimizers' [ADNLPModels](https://jso.dev/ADNLPModels.jl) [@ADNLPModels_jl], GPU acceleration via [ExaModels.jl](https://github.com/exanauts/ExaModels.jl) [@shin2023accelerating], numerical integration from SciML's [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs) [@rackauckas2017differentialequations], and visualization through [Plots.jl](https://docs.juliaplots.org) [@PlotsJL]. + +# Statement of Need + +OptimalControl.jl is, to our knowledge, the only Julia package that unifies both direct and indirect methods for optimal control within a single, coherent framework. + +This unified approach addresses a gap in the current optimal control software landscape. Existing tools are fragmented across programming languages and paradigms. Legacy packages such as [HamPath](https://gitlab.inria.fr/ct/hampath) [@caillau2012differential], [NutoPy](https://ct.gitlabpages.inria.fr/nutopy) [@CAILLAU202213], and [COTCOT](https://github.com/mctao-inria/cotcot) [@bonnard2007second] implement sophisticated indirect methods but rely on Fortran implementations with MATLAB or Python interfaces, leading to complex and less extensible workflows. Proprietary solvers like [GPOPS-II](https://gpops2.com) [@Patterson2014] limit transparency and reproducibility. Open-source tools such as [BOCOP](https://github.com/control-toolbox/bocop) [@Bonnans2017], [ACADO](https://acado.github.io) [@Houska2011], and [acados](https://docs.acados.org) [@Verschueren2021] provide valuable direct method implementations but are not natively integrated into a modern, high-level scientific computing ecosystem. Python-based tools such as [Dymos](https://openmdao.github.io/dymos) [@Falck2021], [Pyomo.DAE](https://pyomo.readthedocs.io/en/stable/modeling_extensions/dae.html) [@Nicholson2018], [do-mpc](https://www.do-mpc.com) [@Fiedler2023], and [GEKKO](https://gekko.readthedocs.io) [@Beal2018] offer complementary capabilities but are similarly limited to direct transcription approaches within the Python ecosystem. + +Within Julia, most existing packages target specific domains: [RobustAndOptimalControl.jl](https://juliacontrol.github.io/RobustAndOptimalControl.jl) for linear systems, [QuantumControl.jl](https://juliaquantumcontrol.github.io/QuantumControl.jl) and [Piccolo.jl](https://github.com/harmoniqs/Piccolo.jl) for quantum optimal control, [DirectTrajectoryOptimization.jl](https://github.com/thowell/DirectTrajectoryOptimization.jl) for trajectory problems, [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] for model predictive control, and [InfiniteOpt.jl](https://infiniteopt.github.io/InfiniteOpt.jl) [@pulsipher2022unifying] for infinite-dimensional optimization. In contrast with InfiniteOpt.jl that is designed as an extension of [JuMP.jl](https://jump.dev/JuMP.jl), our plan is to provide a modeler agnostic approach, able to accept general Julia code and leverage various optimization solvers. Besides, contributing to general-purpose NLP modeling frameworks like JuMP or [CasADi](https://web.casadi.org) [@Andersson2019] would not address the specific needs of optimal control: these tools lack native support for shooting methods based on Pontryagin's Maximum Principle and that heavily rely on differential geometric primitives. + +OptimalControl.jl fills this gap by providing a DSL that matches mathematical notation, multiple discretization schemes and shooting methods, with planned support for homotopy continuation methods. The modeler-solver separation enables complementary use with InfiniteOpt.jl (JuMP-based) through alternative NLP modeling backends (currently ADNLPModels, ExaModels) and solvers. GPU acceleration and an ecosystem with domain-specific applications, tutorials, and benchmarking tools complete the offering. Target users include researchers and engineers working in optimal control, control theorists developing new algorithms, and students learning optimal control through interactive tutorials. + +# State of the Field + +## Comparison with existing software + +OptimalControl.jl requires Julia version 1.10 or later and is registered in the Julia General registry, enabling straightforward installation via `Pkg.add("OptimalControl")`. + +- **Legacy tools (COTCOT, HamPath, NutoPy)**: These Fortran packages excel at indirect methods and homotopy continuation but require multi-language setup (Fortran plus Matlab / Python). OptimalControl.jl provides both direct and indirect methods in pure Julia with straightforward installation via package manager. + +- **Direct method tools (BOCOP, ACADO, GPOPS-II, acados, nosnoc)**: Strong direct method implementations: [GPOPS-II](https://gpops2.com) [@Patterson2014] delivers mature methods with MATLAB and C++ implementations but is proprietary; [acados](https://docs.acados.org) [@Verschueren2021] targets real-time MPC on embedded systems; [nosnoc](https://github.com/nosnoc/nosnoc) [@Nurkanovic2022] specializes in nonsmooth optimal control; [CasADi](https://web.casadi.org) [@Andersson2019], used as symbolic backend by several of these tools, is a general NLP modeler rather than an optimal control solver. OptimalControl.jl offers an open-source alternative with expressive DSL, native Julia ecosystem integration, GPU support, and unified direct and indirect approaches. + +- **Julia packages**: RobustAndOptimalControl.jl targets linear systems; QuantumControl.jl, Piccolo.jl and DirectTrajectoryOptimization.jl serve specific domains; [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] focus on model predictive control. InfiniteOpt.jl addresses a very rich range of problems, including optimization on PDE's or with chance constraintes, focusing on direct transcription methods. OptimalControl.jl works seamlessly on both CPU and GPU, and adds tools to do shooting in a unified framework plus systematic benchmarking through OptimalControlProblems.jl and CTBenchmarks.jl. + +# Illustrative Example + +The following example illustrates both direct and indirect solution approaches for a constrained energy minimization problem. The workflow demonstrates a practical strategy: a direct method on a coarse grid first identifies the problem structure and provides an initial guess for the indirect method, which then computes a solution up to arbitrary precision via shooting based on Pontryagin's Maximum Principle. + +**Definition of the optimal control problem:** + +```julia +# Problem definition: energy-optimal control with state constraint +using OptimalControl +t0 = 0 +tf = 1 +x0 = [-1, 0] +x_target = [0, 0] +v_max = 1.2 +ocp = @def begin + t ∈ [t0, tf], time + x = (q, v) ∈ R², state + u ∈ R, control + x(t0) == x0 # initial condition + x(tf) == x_target # terminal condition + v(t) ≤ v_max # state constraint + ∂(x)(t) == [v(t), u(t)] # dynamics + 0.5∫(u(t)^2) → min # minimize control energy +end +``` + +**Direct method:** The problem is transcribed to an NLP using a midpoint discretization scheme and solved with an interior-point solver. + +```julia +using NLPModelsIpopt +direct_sol = solve(ocp; grid_size=50) +``` + +**Extract initial guess from direct solution:** The initial costate and the two switching times are recovered from the direct solution to initialize the indirect method. + +```julia +t = time_grid(direct_sol) # the time grid as a vector +x = state(direct_sol) # the state as a function of time +p = costate(direct_sol) # the costate as a function of time +p0 = p(t0) # initial costate +g(x) = v_max - x[2] # constraint: g(x) ≥ 0 +I = findall(t -> g(x(t)) ≤ 1e-3, t) # times where constraint is active +t1 = t[first(I)] # entry time +t2 = t[last(I)] # exit time +initial_guess = [p0..., t1, t2] # initial guess for shooting +``` + +**Indirect method:** The indirect method applies Pontryagin's Maximum Principle. The solution has three phases (unconstrained-constrained-unconstrained arcs), requiring definition of Hamiltonian flows for each phase and a shooting function to enforce boundary conditions. + +```julia +using OrdinaryDiffEq, NonlinearSolve + +# Define Hamiltonian flows based on Pontryagin's Maximum Principle +f_interior = Flow(ocp, (x, p) -> p[2]) # u(x, p) is p[2] +f_boundary = Flow(ocp, (x, p) -> 0, # u(x, p) is 0 + (x, u) -> g(x), # when g(x) = 0 (constrained arc) + (x, p) -> p[1]) # associated multiplier is p[1] + +# Shooting function +function shoot!(s, ξ, _) # unused last parameter (required by NonlinearSolve) + p0, t1, t2 = ξ[1:2], ξ[3], ξ[4] + x1, p1 = f_interior(t0, x0, p0, t1) # flow on unconstrained arc [t0, t1] + x2, p2 = f_boundary(t1, x1, p1, t2) # flow on constrained arc [t1, t2] + xf, pf = f_interior(t2, x2, p2, tf) # flow on unconstrained arc [t2, tf] + s[1:2] = xf - x_target # terminal condition + s[3] = g(x1) # entry condition on constraint + s[4] = p1[2] # switching phase condition +end + +# Solve shooting problem +shooting_sol = solve(NonlinearProblem(shoot!, initial_guess)) +p0, t1, t2 = shooting_sol.u[1:2], shooting_sol.u[3], shooting_sol.u[4] +``` + +**Trajectory reconstruction and visualization:** The trajectory is reconstructed by concatenating the three flows using the `*` operator (and indicating the internal times when to concatenate, `t1` and `t2`). Then both solutions are compared visually. + +```julia +# Reconstruct trajectory by concatenating flows +φ = f_interior * (t1, f_boundary) * (t2, f_interior) +indirect_sol = φ((t0, tf), x0, p0; saveat=range(t0, tf, 100)) + +# Compare both solutions +using Plots +plot(direct_sol; label="Direct") +plot!(indirect_sol; label="Indirect", color=2, linestyle=:dash) +``` + +![Comparison of direct and indirect solutions showing state trajectories (position and velocity), costate variables, and control inputs. The three arc structure is very well captured by the first direct solve, allowing convergence to arbitrary precision of the final shooting.](plot.svg){width="100%"} + +# Software Design + +The package architecture balances expressiveness, performance, and extensibility through modular design. The core is organized across internal packages within the [control-toolbox organization](https://github.com/control-toolbox), each hosted as an independent Julia package and registered in the General registry: [CTBase.jl](https://github.com/control-toolbox/CTBase.jl) defines the core types (optimal control models, solutions, initial guesses) and their accessors; [CTParser.jl](https://github.com/control-toolbox/CTParser.jl) implements the `@def` DSL macro; [CTDirect.jl](https://github.com/control-toolbox/CTDirect.jl) handles direct transcription and NLP interfacing; and [CTFlows.jl](https://github.com/control-toolbox/CTFlows.jl) provides Hamiltonian flows and shooting for indirect methods. OptimalControl.jl re-exports these packages as a unified entry point. Contributors interested in a specific functionality can work directly on the relevant sub-package, each of which has its own documentation, tests, and continuous integration. The delegation of specific responsibilities is as follows: + +- **DSL parsing**: [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl) [@MLStyle_jl] enables pattern matching on abstract syntax trees generated from `@def` macro invocations. This design choice separates problem specification from solution methods, and allows a syntax as close as possible to the mathematical description of the problem. + +- **Problem models and solutions**: Structured types represent optimal control models, solutions, and initial guesses. Each type provides textual visualization, accessor methods for introspection, and visual plotting capabilities for solutions. Extensible abstractions enable addition of new problem classes without modifying core code. + +- **Discretization**: Direct transcription converts continuous problems into NLPs. Supporting multiple discretization schemes (Euler, midpoint, trapezoidal, Gauss-Legendre) required careful abstraction to share transcription logic while allowing scheme-specific implementations. + +- **Modelers and solvers**: We chose a clear modeler-solver separation: discretization produces ADNLPModels (able to deal with arbitrary user defined functions) or ExaModels [@shin2023accelerating] instances compatible with multiple NLP solvers (IPOPT via NLPModelsIpopt.jl [@Orban_NLPModelsIpopt_jl], Knitro [@Byrd2006], MadNLP, and [Uno](https://github.com/cvanaret/Uno) [@VanaretLeyffer2026]). These NLP solvers rely on linear solvers such as [MUMPS.jl](https://github.com/JuliaSmoothOptimizers/MUMPS.jl) [@Montoison_MUMPS_jl; @MUMPS:1; @MUMPS:2] for CPU computations or [CUDSS.jl](https://github.com/exanauts/CUDSS.jl) [@CUDSS_nvidia] for GPU acceleration with MadNLP. Automatic differentiation via ForwardDiff.jl [@RevelsLubinPapamarkou2016] and DifferentiationInterface.jl [@dalle2026commoninterfaceautomaticdifferentiation] avoids manual derivative coding. + +- **Indirect methods**: Hamiltonian flows integrate with DifferentialEquations.jl to access adaptive stepping, event handling, and multiple ODE solvers without reimplementation. Shooting methods rely on NonlinearSolve.jl [@pal2024nonlinearsolve] or [MINPACK.jl](https://github.com/sglyon/MINPACK.jl) for root-finding. Future extensions will incorporate homotopy continuation methods leveraging bifurcation analysis tools like [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) [@veltz:hal-02902346]. + +**Key design trade-offs:** + +1. **DSL vs. programmatic API**: We prioritized a mathematical DSL to reduce cognitive load for domain experts, accepting increased parsing complexity handled internally. Currently we do not address optimization of PDE or stochastic systems. + +2. **GPU acceleration strategy**: The modeler-solver separation enables seamless CPU-to-GPU transition. Users simply select the appropriate modeler-solver pair: ExaModels with MadNLP and the CUDSS linear solver for GPU execution. This modular approach minimizes maintenance burden while enabling GPU performance without reimplementing transcription logic. As for now, GPU support is limited to the ExaModels + MadNLP modeler-solver combination. + +3. **Method coverage**: Supporting both direct and indirect approaches increases code complexity but serves distinct user needs: direct methods for constrained problems with many variables, indirect methods for theoretical analysis and smaller problems requiring high accuracy. Both approaches resort to iterative solvers and may converge or not, *e.g.* depending on the initial guess. In the case of optimization solvers, the full output status of the solver is returned allowing *a posteriori* analysis. + +# Research Impact Statement + +OptimalControl.jl has been applied in published research across multiple domains. Independent external adoption demonstrates the package's broader impact: @ferede2025icra used it for drone racing trajectory optimization, @caio2025application for epidemiological models using indirect methods, @morsky2025vaccination for vaccination strategies under social norms, @opmeer2025optimal for optimal harvesting of age-structured populations, and @evangelakos2025fast for fast charging protocols for quantum batteries. + +Research by close collaborators further demonstrates the package's versatility across aerospace (@herasimenka2026lowthrust), epidemiology (@bliman:hal-05194927), quantum control (@beschastnyi2025pulse), microbial growth control (@innerarityimizcoz:hal-05369609), and theoretical optimal control (@bouali:hal-04928858; @lutz:hal-05047678; @bayen2026minimum; @bonnard2026zermelo). + +The [control-toolbox organization](https://control-toolbox.org) hosts domain-specific application packages built on OptimalControl.jl: medical imaging optimization ([MagneticResonanceImaging.jl](https://control-toolbox.org/MagneticResonanceImaging.jl)), gene regulatory networks ([PWLdynamics.jl](https://agustinyabo.github.io/PWLdynamics.jl)), spacecraft orbital transfers ([Kepler.jl](https://control-toolbox.org/Kepler.jl)), epidemiological modeling ([SIRcontrol.jl](https://anasxbouali.github.io/SIRcontrol.jl)), and variational calculus ([CalculusOfVariations.jl](https://control-toolbox.org/CalculusOfVariations.jl)). + +The package serves educational purposes through [Tutorials.jl](https://control-toolbox.org/Tutorials.jl) covering topics from linear-quadratic regulators to Model Predictive Control. These resources are used in academic courses and workshops. [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) provides standardized test problems formulated in both OptimalControl DSL and JuMP, enabling systematic performance comparisons through [CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl). + +Development involves international collaborations with CNES (French space agency), Thales Alenia Space, Inria, and CNRS. The package development began in September 2022, with the first public release in February 2023. As of March 2026, OptimalControl.jl has published more than 40 releases with contributions from multiple developers across the control-toolbox ecosystem packages, demonstrating sustained community engagement. + +# AI Usage Disclosure + +The core software implementation, algorithms, and architectural design of OptimalControl.jl were developed by the authors. Generative AI has been used to assist with code refactoring and generation of unit and integration tests. This paper was drafted by the authors and subsequently revised with AI assistance for restructuring according to JOSS format requirements and language editing. All technical content, examples, and claims reflect the authors' work and judgment. + +# Acknowledgements + +We thank the [control-toolbox community](https://control-toolbox.org/contributors) and the broader Julia ecosystem for contributions that shaped the package design and educational resources. Development has been supported by partnerships with CNES, Thales Alenia Space, Inria, and CNRS. The software is distributed under the MIT license (see [LICENSE](https://github.com/control-toolbox/OptimalControl.jl/blob/main/LICENSE)) and uses centralized GitHub Actions workflows for continuous integration, documentation, and testing across the ecosystem. We welcome community contributions following the guidelines in [CONTRIBUTING.md](https://github.com/control-toolbox/OptimalControl.jl/blob/main/CONTRIBUTING.md). + +# References diff --git a/joss/plot.svg b/joss/plot.svg new file mode 100644 index 00000000..69c4a225 --- /dev/null +++ b/joss/plot.svg @@ -0,0 +1,4354 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From ec5acdc0cf1ef5bda9a6628804b63b28eb641f2b Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 15 Apr 2026 17:54:29 +0200 Subject: [PATCH 02/29] fix spell checks --- _typos.toml | 1 + joss/paper.md | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/_typos.toml b/_typos.toml index 6263e4be..3db4841f 100644 --- a/_typos.toml +++ b/_typos.toml @@ -2,6 +2,7 @@ locale = "en" extend-ignore-re = [ "ded", + "ois", ] [files] diff --git a/joss/paper.md b/joss/paper.md index 913604b8..22d72fa6 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -68,7 +68,7 @@ OptimalControl.jl requires Julia version 1.10 or later and is registered in the - **Direct method tools (BOCOP, ACADO, GPOPS-II, acados, nosnoc)**: Strong direct method implementations: [GPOPS-II](https://gpops2.com) [@Patterson2014] delivers mature methods with MATLAB and C++ implementations but is proprietary; [acados](https://docs.acados.org) [@Verschueren2021] targets real-time MPC on embedded systems; [nosnoc](https://github.com/nosnoc/nosnoc) [@Nurkanovic2022] specializes in nonsmooth optimal control; [CasADi](https://web.casadi.org) [@Andersson2019], used as symbolic backend by several of these tools, is a general NLP modeler rather than an optimal control solver. OptimalControl.jl offers an open-source alternative with expressive DSL, native Julia ecosystem integration, GPU support, and unified direct and indirect approaches. -- **Julia packages**: RobustAndOptimalControl.jl targets linear systems; QuantumControl.jl, Piccolo.jl and DirectTrajectoryOptimization.jl serve specific domains; [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] focus on model predictive control. InfiniteOpt.jl addresses a very rich range of problems, including optimization on PDE's or with chance constraintes, focusing on direct transcription methods. OptimalControl.jl works seamlessly on both CPU and GPU, and adds tools to do shooting in a unified framework plus systematic benchmarking through OptimalControlProblems.jl and CTBenchmarks.jl. +- **Julia packages**: RobustAndOptimalControl.jl targets linear systems; QuantumControl.jl, Piccolo.jl and DirectTrajectoryOptimization.jl serve specific domains; [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] focus on model predictive control. InfiniteOpt.jl addresses a very rich range of problems, including optimization on PDE's or with chance constraints, focusing on direct transcription methods. OptimalControl.jl works seamlessly on both CPU and GPU, and adds tools to do shooting in a unified framework plus systematic benchmarking through OptimalControlProblems.jl and CTBenchmarks.jl. # Illustrative Example From d4fa5495fef0fbe537b26fe0480c3e60f8bb1af1 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 15 Apr 2026 17:55:29 +0200 Subject: [PATCH 03/29] change trigger breakage --- .github/workflows/Breakage.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/Breakage.yml b/.github/workflows/Breakage.yml index d3af6eff..d8066923 100644 --- a/.github/workflows/Breakage.yml +++ b/.github/workflows/Breakage.yml @@ -9,7 +9,7 @@ on: jobs: break-pkg: - if: ${{ ! contains(github.event.pull_request.labels.*.name, 'run breakage applications') }} + if: contains(github.event.pull_request.labels.*.name, 'run breakage') strategy: fail-fast: false matrix: From d64110c0ed47c63d70106d9771f902362174314a Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 15 Apr 2026 17:56:46 +0200 Subject: [PATCH 04/29] foo --- .github/workflows/JOSS.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.github/workflows/JOSS.yml b/.github/workflows/JOSS.yml index a94de1a6..23ca10d2 100644 --- a/.github/workflows/JOSS.yml +++ b/.github/workflows/JOSS.yml @@ -3,7 +3,7 @@ name: Compile JOSS paper on: push: paths: - - 'joss' # Se déclenche uniquement pour les changements dans le dossier paper + - 'joss/**' # Se déclenche uniquement pour les changements dans le dossier joss jobs: paper: From ce1d25f85f16e90d3e5ed845949957244c5572aa Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 15 Apr 2026 17:57:52 +0200 Subject: [PATCH 05/29] foo --- joss/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index 22d72fa6..45a54fe3 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -201,4 +201,4 @@ The core software implementation, algorithms, and architectural design of Optima We thank the [control-toolbox community](https://control-toolbox.org/contributors) and the broader Julia ecosystem for contributions that shaped the package design and educational resources. Development has been supported by partnerships with CNES, Thales Alenia Space, Inria, and CNRS. The software is distributed under the MIT license (see [LICENSE](https://github.com/control-toolbox/OptimalControl.jl/blob/main/LICENSE)) and uses centralized GitHub Actions workflows for continuous integration, documentation, and testing across the ecosystem. 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@Inbook{Byrd2006, @@ -503,7 +504,8 @@ @misc{shin2023accelerating year={2023}, eprint={2307.16830}, archivePrefix={arXiv}, - primaryClass={math.OC} + primaryClass={math.OC}, + doi="10.2139/ssrn.4601442" } @software{Montoison_MUMPS_jl, @@ -523,7 +525,8 @@ @article{MUMPS:1 volume = {23}, number = {1}, year = {2001}, - pages = {15--41} + pages = {15--41}, + doi = {10.1137/s0895479899358194} } @article{MUMPS:2, @@ -567,7 +570,8 @@ @article{Nurkanovic2022 volume={6}, pages={3110--3115}, year={2022}, - publisher={IEEE} + publisher={IEEE}, + doi={10.1109/lcsys.2022.3181800} } @unpublished{VanaretLeyffer2026, From 17c5d951eb985bb78a340a6d67b671753637b353 Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Thu, 16 Apr 2026 07:25:21 +0000 Subject: [PATCH 08/29] chore: update paper.pdf --- joss/paper.pdf | Bin 348779 -> 348997 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/joss/paper.pdf b/joss/paper.pdf index 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Replace illustrative example with Zenodo DOI reference - Move illustrative example to companion repository (joss-oc-example) - Add bib entry for Zenodo DOI 10.5281/zenodo.19663650 - Simplify Illustrative Example section to reference companion repo - Remove orphaned ## heading in State of the Field section - Delete plot.svg (no longer needed) --- joss/paper.bib | 10 + joss/paper.md | 91 +- joss/plot.svg | 4354 ------------------------------------------------ 3 files changed, 12 insertions(+), 4443 deletions(-) delete mode 100644 joss/plot.svg diff --git a/joss/paper.bib b/joss/paper.bib index 7b63baa4..9326c820 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -1,4 +1,14 @@ +@software{joss_oc_example, + author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre and Sed, Sophia}, + title = {joss-oc-example: illustrative example companion to the {OptimalControl.jl} {JOSS} paper}, + version = {v1.0.0}, + year = {2026}, + publisher = {Zenodo}, + doi = {10.5281/zenodo.19663650}, + url = {https://doi.org/10.5281/zenodo.19663650} +} + @article{rackauckas2017differentialequations, title={Differentialequations.jl--a performant and feature-rich ecosystem for solving differential equations in julia}, author={Rackauckas, Christopher and Nie, Qing}, diff --git a/joss/paper.md b/joss/paper.md index 45a54fe3..60b719e3 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -60,9 +60,7 @@ OptimalControl.jl fills this gap by providing a DSL that matches mathematical no # State of the Field -## Comparison with existing software - -OptimalControl.jl requires Julia version 1.10 or later and is registered in the Julia General registry, enabling straightforward installation via `Pkg.add("OptimalControl")`. +OptimalControl.jl requires Julia version 1.10 or later and is registered in the Julia General registry, enabling straightforward installation via `Pkg.add("OptimalControl")`. We compare it below with existing software. - **Legacy tools (COTCOT, HamPath, NutoPy)**: These Fortran packages excel at indirect methods and homotopy continuation but require multi-language setup (Fortran plus Matlab / Python). OptimalControl.jl provides both direct and indirect methods in pure Julia with straightforward installation via package manager. @@ -72,92 +70,7 @@ OptimalControl.jl requires Julia version 1.10 or later and is registered in the # Illustrative Example -The following example illustrates both direct and indirect solution approaches for a constrained energy minimization problem. The workflow demonstrates a practical strategy: a direct method on a coarse grid first identifies the problem structure and provides an initial guess for the indirect method, which then computes a solution up to arbitrary precision via shooting based on Pontryagin's Maximum Principle. - -**Definition of the optimal control problem:** - -```julia -# Problem definition: energy-optimal control with state constraint -using OptimalControl -t0 = 0 -tf = 1 -x0 = [-1, 0] -x_target = [0, 0] -v_max = 1.2 -ocp = @def begin - t ∈ [t0, tf], time - x = (q, v) ∈ R², state - u ∈ R, control - x(t0) == x0 # initial condition - x(tf) == x_target # terminal condition - v(t) ≤ v_max # state constraint - ∂(x)(t) == [v(t), u(t)] # dynamics - 0.5∫(u(t)^2) → min # minimize control energy -end -``` - -**Direct method:** The problem is transcribed to an NLP using a midpoint discretization scheme and solved with an interior-point solver. - -```julia -using NLPModelsIpopt -direct_sol = solve(ocp; grid_size=50) -``` - -**Extract initial guess from direct solution:** The initial costate and the two switching times are recovered from the direct solution to initialize the indirect method. - -```julia -t = time_grid(direct_sol) # the time grid as a vector -x = state(direct_sol) # the state as a function of time -p = costate(direct_sol) # the costate as a function of time -p0 = p(t0) # initial costate -g(x) = v_max - x[2] # constraint: g(x) ≥ 0 -I = findall(t -> g(x(t)) ≤ 1e-3, t) # times where constraint is active -t1 = t[first(I)] # entry time -t2 = t[last(I)] # exit time -initial_guess = [p0..., t1, t2] # initial guess for shooting -``` - -**Indirect method:** The indirect method applies Pontryagin's Maximum Principle. The solution has three phases (unconstrained-constrained-unconstrained arcs), requiring definition of Hamiltonian flows for each phase and a shooting function to enforce boundary conditions. - -```julia -using OrdinaryDiffEq, NonlinearSolve - -# Define Hamiltonian flows based on Pontryagin's Maximum Principle -f_interior = Flow(ocp, (x, p) -> p[2]) # u(x, p) is p[2] -f_boundary = Flow(ocp, (x, p) -> 0, # u(x, p) is 0 - (x, u) -> g(x), # when g(x) = 0 (constrained arc) - (x, p) -> p[1]) # associated multiplier is p[1] - -# Shooting function -function shoot!(s, ξ, _) # unused last parameter (required by NonlinearSolve) - p0, t1, t2 = ξ[1:2], ξ[3], ξ[4] - x1, p1 = f_interior(t0, x0, p0, t1) # flow on unconstrained arc [t0, t1] - x2, p2 = f_boundary(t1, x1, p1, t2) # flow on constrained arc [t1, t2] - xf, pf = f_interior(t2, x2, p2, tf) # flow on unconstrained arc [t2, tf] - s[1:2] = xf - x_target # terminal condition - s[3] = g(x1) # entry condition on constraint - s[4] = p1[2] # switching phase condition -end - -# Solve shooting problem -shooting_sol = solve(NonlinearProblem(shoot!, initial_guess)) -p0, t1, t2 = shooting_sol.u[1:2], shooting_sol.u[3], shooting_sol.u[4] -``` - -**Trajectory reconstruction and visualization:** The trajectory is reconstructed by concatenating the three flows using the `*` operator (and indicating the internal times when to concatenate, `t1` and `t2`). Then both solutions are compared visually. - -```julia -# Reconstruct trajectory by concatenating flows -φ = f_interior * (t1, f_boundary) * (t2, f_interior) -indirect_sol = φ((t0, tf), x0, p0; saveat=range(t0, tf, 100)) - -# Compare both solutions -using Plots -plot(direct_sol; label="Direct") -plot!(indirect_sol; label="Indirect", color=2, linestyle=:dash) -``` - -![Comparison of direct and indirect solutions showing state trajectories (position and velocity), costate variables, and control inputs. The three arc structure is very well captured by the first direct solve, allowing convergence to arbitrary precision of the final shooting.](plot.svg){width="100%"} +A self-contained illustrative example is provided as a companion repository [@joss_oc_example], archived on Zenodo. It combines direct and indirect solution approaches for a constrained energy minimization problem: a direct method on a coarse grid identifies the three-arc structure (unconstrained–constrained–unconstrained) and initializes a shooting method based on Pontryagin's Maximum Principle, which then converges to arbitrary precision. # Software Design diff --git a/joss/plot.svg b/joss/plot.svg deleted file mode 100644 index 69c4a225..00000000 --- a/joss/plot.svg +++ /dev/null @@ -1,4354 +0,0 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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documentation and README; add Testing and quality assurance paragraph to JOSS paper --- README.template.md | 8 ++++++++ docs/src/index.md | 8 ++++++++ joss/paper.md | 4 +++- 3 files changed, 19 insertions(+), 1 deletion(-) diff --git a/README.template.md b/README.template.md index 8aa8ce79..a5d98482 100644 --- a/README.template.md +++ b/README.template.md @@ -13,6 +13,10 @@ The OptimalControl.jl package is part of the [control-toolbox ecosystem](https:/ +## Motivation + +The guiding philosophy of OptimalControl.jl is to offer, to our knowledge, the only Julia package that unifies both direct and indirect methods for optimal control within a single, coherent framework. This fills a gap in a landscape where existing tools are fragmented across programming languages and paradigms, and are usually restricted to a single family of methods. The package provides a domain-specific language that closely matches mathematical notation, together with multiple discretization schemes and shooting methods, and planned support for homotopy continuation methods. Its modeler–solver separation makes it agnostic to the underlying NLP modeling backend and optimization solver, and enables seamless execution on both CPU and GPU with minimal user intervention. Combined with an ecosystem of domain-specific applications, tutorials, and benchmarking tools, this design targets researchers and engineers working in optimal control, control theorists developing new algorithms, and students learning the field through interactive tutorials. + ## Basic usage Let us model and solve a simple optimal control problem, then plot the solution: @@ -39,6 +43,10 @@ plot(sol) For more details about this problem, please check the basic example presented in the [documentation](https://control-toolbox.org/OptimalControl.jl). +## Testing + +OptimalControl.jl is the umbrella package of a multi-repository ecosystem with a layered testing strategy: each sub-package has its own suite combining unit tests, integration tests, and code-quality checks, while the umbrella package adds strong end-to-end tests solving complete problems by both direct and indirect methods. Continuous integration runs on Linux, macOS, and Windows, on both CPU and GPU, through reusable workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions), with code coverage tracked on Codecov and downstream packages guarded against regressions through breakage tests. Part of the test code is written with AI assistance, always under human review. + ## Citing us If you use OptimalControl.jl in your work, please cite us: diff --git a/docs/src/index.md b/docs/src/index.md index b57b4edf..a5aa7d75 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -2,6 +2,10 @@ The OptimalControl.jl package is the root package of the [control-toolbox ecosystem](https://github.com/control-toolbox). The control-toolbox ecosystem gathers Julia packages for mathematical control and applications. It aims to provide tools to model and solve optimal control problems with ordinary differential equations by direct and indirect methods, both on CPU and GPU. +## Motivation + +The guiding philosophy of OptimalControl.jl is to offer, to our knowledge, the only Julia package that unifies both direct and indirect methods for optimal control within a single, coherent framework. This fills a gap in a landscape where existing tools are fragmented across programming languages and paradigms, and are usually restricted to a single family of methods. The package provides a domain-specific language that closely matches mathematical notation, together with multiple discretization schemes and shooting methods, and planned support for homotopy continuation methods. Its modeler–solver separation makes it agnostic to the underlying NLP modeling backend and optimization solver, and enables seamless execution on both CPU and GPU with minimal user intervention. Combined with an ecosystem of domain-specific applications, tutorials, and benchmarking tools, this design targets researchers and engineers working in optimal control, control theorists developing new algorithms, and students learning the field through interactive tutorials. + ## Installation To install OptimalControl.jl, please [open Julia's interactive session (known as REPL)](https://docs.julialang.org/en/v1/manual/getting-started) and use the Julia package manager: @@ -124,6 +128,10 @@ If you want to ask a question, feel free to start a discussion [here](https://gi If you want to add an application or a package to the control-toolbox ecosystem, please follow this [set up tutorial](https://github.com/orgs/control-toolbox/discussions/65). +## Testing + +OptimalControl.jl is the umbrella package of a multi-repository ecosystem, and testing is organized in layers. Each sub-package (`CTBase`, `CTParser`, `CTModels`, `CTDirect`, `CTSolvers`, `CTFlows`) has its own test suite combining unit tests, integration tests, and code-quality checks (e.g. with [Aqua.jl](https://github.com/JuliaTesting/Aqua.jl)). At the umbrella level, OptimalControl.jl adds strong end-to-end integration tests that solve complete optimal control problems with both direct and indirect methods. Continuous integration runs on Linux, macOS, and Windows, on both CPU and GPU (via a self-hosted CUDA runner), through reusable workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions). Code coverage is tracked on [Codecov](https://codecov.io), downstream packages are guarded against regressions through dedicated breakage tests, and beta versions are distributed during development via a local registry, [ct-registry](https://github.com/control-toolbox/ct-registry). Part of the test code is written with the help of AI agents, always under human review. + ## Reproducibility ```@setup main diff --git a/joss/paper.md b/joss/paper.md index 60b719e3..0ddccca7 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -86,6 +86,8 @@ The package architecture balances expressiveness, performance, and extensibility - **Indirect methods**: Hamiltonian flows integrate with DifferentialEquations.jl to access adaptive stepping, event handling, and multiple ODE solvers without reimplementation. Shooting methods rely on NonlinearSolve.jl [@pal2024nonlinearsolve] or [MINPACK.jl](https://github.com/sglyon/MINPACK.jl) for root-finding. Future extensions will incorporate homotopy continuation methods leveraging bifurcation analysis tools like [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) [@veltz:hal-02902346]. +- **Testing and quality assurance**: The multi-repository structure is matched by a layered testing strategy. Each sub-package is tested independently, combining unit tests, integration tests, and code-quality checks (e.g. with Aqua.jl), while OptimalControl.jl adds strong end-to-end integration tests that solve complete optimal control problems by both direct and indirect methods. Continuous integration runs across Linux, macOS, and Windows, on both CPU and GPU (through a self-hosted CUDA runner), using reusable GitHub Actions workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions) and shared across the ecosystem. Code coverage is tracked on Codecov, downstream packages and applications are guarded against regressions through dedicated breakage tests triggered on pull requests, and beta versions are distributed during development via a local registry, [ct-registry](https://github.com/control-toolbox/ct-registry). Non-regression on complex problems is increasingly driven by OptimalControlProblems.jl [@OptimalControlProblems_jl], used as a curated problem bank. + **Key design trade-offs:** 1. **DSL vs. programmatic API**: We prioritized a mathematical DSL to reduce cognitive load for domain experts, accepting increased parsing complexity handled internally. Currently we do not address optimization of PDE or stochastic systems. @@ -112,6 +114,6 @@ The core software implementation, algorithms, and architectural design of Optima # Acknowledgements -We thank the [control-toolbox community](https://control-toolbox.org/contributors) and the broader Julia ecosystem for contributions that shaped the package design and educational resources. Development has been supported by partnerships with CNES, Thales Alenia Space, Inria, and CNRS. The software is distributed under the MIT license (see [LICENSE](https://github.com/control-toolbox/OptimalControl.jl/blob/main/LICENSE)) and uses centralized GitHub Actions workflows for continuous integration, documentation, and testing across the ecosystem. We welcome community contributions following the guidelines in [CONTRIBUTING.md](https://github.com/control-toolbox/OptimalControl.jl/blob/main/CONTRIBUTING.md). +We thank the [control-toolbox community](https://control-toolbox.org/contributors) and the broader Julia ecosystem for contributions that shaped the package design and educational resources. Development has been supported by partnerships with CNES, Thales Alenia Space, Inria, and CNRS. The software is distributed under the MIT license (see [LICENSE](https://github.com/control-toolbox/OptimalControl.jl/blob/main/LICENSE)). 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OptimalControlProblems.jl --- joss/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index 0ddccca7..11b12a45 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -86,7 +86,7 @@ The package architecture balances expressiveness, performance, and extensibility - **Indirect methods**: Hamiltonian flows integrate with DifferentialEquations.jl to access adaptive stepping, event handling, and multiple ODE solvers without reimplementation. Shooting methods rely on NonlinearSolve.jl [@pal2024nonlinearsolve] or [MINPACK.jl](https://github.com/sglyon/MINPACK.jl) for root-finding. Future extensions will incorporate homotopy continuation methods leveraging bifurcation analysis tools like [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) [@veltz:hal-02902346]. -- **Testing and quality assurance**: The multi-repository structure is matched by a layered testing strategy. Each sub-package is tested independently, combining unit tests, integration tests, and code-quality checks (e.g. with Aqua.jl), while OptimalControl.jl adds strong end-to-end integration tests that solve complete optimal control problems by both direct and indirect methods. Continuous integration runs across Linux, macOS, and Windows, on both CPU and GPU (through a self-hosted CUDA runner), using reusable GitHub Actions workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions) and shared across the ecosystem. Code coverage is tracked on Codecov, downstream packages and applications are guarded against regressions through dedicated breakage tests triggered on pull requests, and beta versions are distributed during development via a local registry, [ct-registry](https://github.com/control-toolbox/ct-registry). Non-regression on complex problems is increasingly driven by OptimalControlProblems.jl [@OptimalControlProblems_jl], used as a curated problem bank. +- **Testing and quality assurance**: The multi-repository structure is matched by a layered testing strategy. Each sub-package is tested independently, combining unit tests, integration tests, and code-quality checks, while OptimalControl.jl adds strong end-to-end integration tests that solve complete optimal control problems by both direct and indirect methods. Continuous integration runs across Linux, macOS, and Windows, on both CPU and GPU (through a self-hosted CUDA runner), using reusable GitHub Actions workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions) and shared across the ecosystem. Code coverage is tracked on Codecov, downstream packages and applications are guarded against regressions through dedicated breakage tests triggered on pull requests, and beta versions are distributed during development via a local registry, [ct-registry](https://github.com/control-toolbox/ct-registry). Non-regression on complex problems is increasingly driven by [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl), used as a curated problem bank. **Key design trade-offs:** From daec5bd9d9290894bffed3f9c19626cb767ec11b Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Thu, 4 Jun 2026 11:08:02 +0000 Subject: [PATCH 14/29] chore: update paper.pdf --- joss/paper.pdf | Bin 262744 -> 262672 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/joss/paper.pdf b/joss/paper.pdf index 662badc6eac13582b65ac7851afd7b383d9d902f..73882ea39d47dd15f7ff3ff2d6c4ab928fd9f5ad 100644 GIT binary patch delta 15960 zcmajGV{qV2@b9~^ZQHh!&BnHEY;6Bx+qP|MW7~E%*2cQe|D0R*ytudO&Zlasr+WHb z*L3x_de(xGfS+vU$ zB+=triuXHWw%h(>+pJ-IGhap->~2UZMTbv~m5UcC=HL{>e26-t$>^zmJ@0{eK&X=W_eBm{qVkT26)ljawf?%)TtoU$uiPkDGN*Dyaru zbPTZj(p4Ls$c@O$DpmL9=bwIDsH^(?H>)7iN_|-#SC@)CZLE!l4-Kn=lr2G>((Yz- z1M{*5(+C>UChLMiIek*Ag2ewcCKu4NrVyaiBQ%Q=I64np9Y6#1QNjPf82-CTuC7Y2 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zm+&6~NMihqOz3w0Qr7l=&GV0n1}t>J8)dC1d%H=XP%D2w#)IPp+^Mz|nG&MpF_n@`9~0_Y-sVgy%g{J-}lp&jHp!G?~XzS8R!`jdEZ z?G!zIv{xnx_xbB6Z_&;~X#inj01W$rwgF2!r}qv*ld6{W*DB&GLe9?qtGQMLT(%k_uY%NLX~KQY3KcM?buq^{FF+Oe0g>TtgFs`yw@p(W`{eHaz_# zX8sX0N0=P(Bl%RcwL1G+)#9XExsV3r$FQ$?{Q|3TWDC7G`2zva$rg^@VK-;RrP wo;j*lcXd6CGypz8`z)6N&5JtQgLwt);o;Y%9fLv;!?81S!ckI6C`rQo9|i_FCjbBd From ec54a5c65ebca6dbbd9522e407aff2360c4fff67 Mon Sep 17 00:00:00 2001 From: ocots <66357348+ocots@users.noreply.github.com> Date: Thu, 4 Jun 2026 11:11:06 +0000 Subject: [PATCH 15/29] Update README (2026-06-04) with latest ABOUT.md, INSTALL.md, CONTRIBUTING.md and badges --- README.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/README.md b/README.md index 7430d575..5ce07b00 100644 --- a/README.md +++ b/README.md @@ -59,6 +59,10 @@ pkg> add OptimalControl >[!NOTE] >The package requires Julia version 1.10 or later. +## Motivation + +The guiding philosophy of OptimalControl.jl is to offer, to our knowledge, the only Julia package that unifies both direct and indirect methods for optimal control within a single, coherent framework. This fills a gap in a landscape where existing tools are fragmented across programming languages and paradigms, and are usually restricted to a single family of methods. The package provides a domain-specific language that closely matches mathematical notation, together with multiple discretization schemes and shooting methods, and planned support for homotopy continuation methods. Its modeler–solver separation makes it agnostic to the underlying NLP modeling backend and optimization solver, and enables seamless execution on both CPU and GPU with minimal user intervention. Combined with an ecosystem of domain-specific applications, tutorials, and benchmarking tools, this design targets researchers and engineers working in optimal control, control theorists developing new algorithms, and students learning the field through interactive tutorials. + ## Basic usage Let us model and solve a simple optimal control problem, then plot the solution: @@ -85,6 +89,10 @@ plot(sol) For more details about this problem, please check the basic example presented in the [documentation](https://control-toolbox.org/OptimalControl.jl). +## Testing + +OptimalControl.jl is the umbrella package of a multi-repository ecosystem with a layered testing strategy: each sub-package has its own suite combining unit tests, integration tests, and code-quality checks, while the umbrella package adds strong end-to-end tests solving complete problems by both direct and indirect methods. Continuous integration runs on Linux, macOS, and Windows, on both CPU and GPU, through reusable workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions), with code coverage tracked on Codecov and downstream packages guarded against regressions through breakage tests. Part of the test code is written with AI assistance, always under human review. + ## Citing us If you use OptimalControl.jl in your work, please cite us: From 8430f2e83f9c4fe33be749a5251b263a6d81e106 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 11 Jun 2026 17:04:55 +0200 Subject: [PATCH 16/29] docs: add disclaimer about non-Hamiltonian flows limitation - joss/paper.md: append sentence to the Indirect methods bullet in the Software Design section noting that indirect methods are currently limited to Hamiltonian flows (u(x,p)) and that support for non-Hamiltonian flows is under active development - docs/src/manual-flow-ocp.md: add a prominent note admonition at the top of the flow-from-OCP tutorial, before any code example, explaining the same limitation and listing the planned extensions (open-loop u(t) and state-feedback u(x)) --- docs/src/manual-flow-ocp.md | 3 +++ joss/paper.md | 2 +- 2 files changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/src/manual-flow-ocp.md b/docs/src/manual-flow-ocp.md index 7df91da0..10f5c224 100644 --- a/docs/src/manual-flow-ocp.md +++ b/docs/src/manual-flow-ocp.md @@ -2,6 +2,9 @@ In this tutorial, we explain the `Flow` function, in particular to compute flows from an optimal control problem. +!!! note "Current limitation" + Currently, from an optimal control problem, only **Hamiltonian flows** can be constructed, i.e. the control law must be provided in **feedback form depending on both state and costate**: `u(x, p)`. An active refactoring is under way to extend support to non-Hamiltonian flows, in particular open-loop control laws `u(t)` and state feedback control laws `u(x)`. + ## Basic usage Les us define a basic optimal control problem. diff --git a/joss/paper.md b/joss/paper.md index 11b12a45..e9c043d9 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -84,7 +84,7 @@ The package architecture balances expressiveness, performance, and extensibility - **Modelers and solvers**: We chose a clear modeler-solver separation: discretization produces ADNLPModels (able to deal with arbitrary user defined functions) or ExaModels [@shin2023accelerating] instances compatible with multiple NLP solvers (IPOPT via NLPModelsIpopt.jl [@Orban_NLPModelsIpopt_jl], Knitro [@Byrd2006], MadNLP, and [Uno](https://github.com/cvanaret/Uno) [@VanaretLeyffer2026]). These NLP solvers rely on linear solvers such as [MUMPS.jl](https://github.com/JuliaSmoothOptimizers/MUMPS.jl) [@Montoison_MUMPS_jl; @MUMPS:1; @MUMPS:2] for CPU computations or [CUDSS.jl](https://github.com/exanauts/CUDSS.jl) [@CUDSS_nvidia] for GPU acceleration with MadNLP. Automatic differentiation via ForwardDiff.jl [@RevelsLubinPapamarkou2016] and DifferentiationInterface.jl [@dalle2026commoninterfaceautomaticdifferentiation] avoids manual derivative coding. -- **Indirect methods**: Hamiltonian flows integrate with DifferentialEquations.jl to access adaptive stepping, event handling, and multiple ODE solvers without reimplementation. Shooting methods rely on NonlinearSolve.jl [@pal2024nonlinearsolve] or [MINPACK.jl](https://github.com/sglyon/MINPACK.jl) for root-finding. Future extensions will incorporate homotopy continuation methods leveraging bifurcation analysis tools like [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) [@veltz:hal-02902346]. +- **Indirect methods**: Hamiltonian flows integrate with DifferentialEquations.jl to access adaptive stepping, event handling, and multiple ODE solvers without reimplementation. Shooting methods rely on NonlinearSolve.jl [@pal2024nonlinearsolve] or [MINPACK.jl](https://github.com/sglyon/MINPACK.jl) for root-finding. Future extensions will incorporate homotopy continuation methods leveraging bifurcation analysis tools like [BifurcationKit.jl](https://github.com/bifurcationkit/BifurcationKit.jl) [@veltz:hal-02902346]. Currently, indirect methods are limited to Hamiltonian flows, where the feedback control law depends on both state and costate; support for non-Hamiltonian flows (open-loop or state-feedback control laws) is under active development. - **Testing and quality assurance**: The multi-repository structure is matched by a layered testing strategy. Each sub-package is tested independently, combining unit tests, integration tests, and code-quality checks, while OptimalControl.jl adds strong end-to-end integration tests that solve complete optimal control problems by both direct and indirect methods. Continuous integration runs across Linux, macOS, and Windows, on both CPU and GPU (through a self-hosted CUDA runner), using reusable GitHub Actions workflows centralized in [CTActions](https://github.com/control-toolbox/CTActions) and shared across the ecosystem. Code coverage is tracked on Codecov, downstream packages and applications are guarded against regressions through dedicated breakage tests triggered on pull requests, and beta versions are distributed during development via a local registry, [ct-registry](https://github.com/control-toolbox/ct-registry). Non-regression on complex problems is increasingly driven by [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl), used as a curated problem bank. 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zS%Gtn{7UWYFnsNM$`1%}6Uc)bnr;j_XU55U8uN}%BCN&etR7CTiD2HkNh%}>QrEHL zNV389SK^ClK;__aFyRUKza<^~KN1W6AMphLm27aj1jAw^bpe&PM03iFigkI+6R=<8 z3_JJ;d?c~>S<0Rdf6=iZZ*7sR9w6zu7cQ7yPRb{?W1wrAlVRACm(_|BC)?0@bv~F>8uqDoN^oUwfOLA0o(4Bx(me z(sXhwT`5{EOV?{;7#}D%rnmr#$5_$ZDqVdM>6=0stmaOp$aTKvugsqj%C{(R@cZoK zGYyExTjdzD#R>QkMe{5|-hdKiz(`sMRiosmghCz$B^g~MfxNI^OdTEHFxRL8i@2SO z7`O|W$3_8eqYO_*DM>5DuiGg*LOeSXhXpz;@=A3-T+NBq%btnY(5+Xw`>kBRTlZ=n za-)tZxc}#4{U6AoE;%XBH#Kk<>cR9{IcmxDS~zt>?lSa&+}q^sd1}+WCx)lhhAoy8 z1iUp`!2x;DWm94|=O`Wir8q^$>)3Ar`g}`>mlNN#b(IkK!7=6IS!8NQUrJ>VDgRwx zK;pKEP5VIh*;sbKy9c|WFukL)nuP1bgu(be$z;dZuI<08yvn#QVAb+Y?f2Z#>P8W9n7eGQub0x%DWHvj+t From 09fa707cff5c54591df8699f4acdc94a69a415b6 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 11 Jun 2026 17:47:10 +0200 Subject: [PATCH 18/29] joss: address reviewer 2 first-round comments - AI disclosure: name Claude Sonnet 4.6 and Claude Opus 4.8 by Anthropic - GPU claims: replace "seamless" with accurate language; clarify NVIDIA-only constraint and ExaModels + MadNLP requirement in Summary, State of the Field, and GPU trade-off sections - JuliaCon 2023: add @caillau2023juliacon entry to paper.bib and cite it in the Research Impact section - "our plan is": rephrase to present tense ("our package provides") - MATLAB: already fixed by author (Matlab -> MATLAB in State of the Field) --- joss/paper.bib | 7 +++++++ joss/paper.md | 14 +++++++------- 2 files changed, 14 insertions(+), 7 deletions(-) diff --git a/joss/paper.bib b/joss/paper.bib index 9326c820..66b01b29 100644 --- a/joss/paper.bib +++ b/joss/paper.bib @@ -1,4 +1,11 @@ +@misc{caillau2023juliacon, + author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre and Sed, Sophia}, + title = {{OptimalControl.jl}: a {Julia} package to model and solve optimal control problems}, + year = {2023}, + howpublished = {JuliaCon 2023, Cambridge, MA. Talk and abstract: \url{https://pretalx.com/juliacon2023/talk/HDC8F7/}. Video recording: \url{https://www.youtube.com/watch?v=RYUtVnzLj5k}} +} + @software{joss_oc_example, author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre and Sed, Sophia}, title = {joss-oc-example: illustrative example companion to the {OptimalControl.jl} {JOSS} paper}, diff --git a/joss/paper.md b/joss/paper.md index 11b12a45..bdcaa469 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -44,7 +44,7 @@ archive_doi: 10.5281/zenodo.13336563 [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) [@OptimalControl_jl] is a Julia [@Bezanson2017] package for modeling and solving optimal control problems governed by ordinary differential equations (ODEs). As the core of the [control-toolbox ecosystem](https://control-toolbox.org), it provides a unified framework that supports both direct and indirect solution methods with applications spanning aerospace, medical imaging, epidemiology, and quantum control. -The package features an expressive domain-specific language (DSL) built around the `@def` macro, enabling users to define control problems using notation that closely resembles standard mathematical formulations. Problems are solved through direct transcription, converting the continuous problem into a nonlinear program (NLP) using discretization schemes including Euler, trapezoidal, midpoint, and high-order Gauss-Legendre collocation. Alternatively, indirect shooting methods based on Pontryagin's Maximum Principle can be employed. The architecture relies on a modeler-solver separation that provides a modular and extensible foundation, enabling seamless execution on both CPU and GPU with minimal user intervention. +The package features an expressive domain-specific language (DSL) built around the `@def` macro, enabling users to define control problems using notation that closely resembles standard mathematical formulations. Problems are solved through direct transcription, converting the continuous problem into a nonlinear program (NLP) using discretization schemes including Euler, trapezoidal, midpoint, and high-order Gauss-Legendre collocation. Alternatively, indirect shooting methods based on Pontryagin's Maximum Principle can be employed. The architecture relies on a modeler-solver separation that provides a modular and extensible foundation, enabling GPU execution (currently on NVIDIA hardware via ExaModels.jl and MadNLP.jl) with minimal user intervention alongside standard CPU solvers. The ecosystem includes extensive [tutorial resources](https://control-toolbox.org/Tutorials.jl), a benchmark problem collection ([OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) [@OptimalControlProblems_jl] with formulations in OptimalControl DSL and [JuMP](https://jump.dev/JuMP.jl) [@Lubin2023]), and performance comparison tools ([CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl)). Integration with Julia's ecosystem enables access to state-of-the-art tools: NLP solvers [IPOPT](https://coin-or.github.io/Ipopt) [@Wachter2006] and [MadNLP.jl](https://github.com/MadNLP/MadNLP.jl) [@SHIN2024110651; @SHIN2021693], automatic differentiation and NLP modeling through JuliaSmoothOptimizers' [ADNLPModels](https://jso.dev/ADNLPModels.jl) [@ADNLPModels_jl], GPU acceleration via [ExaModels.jl](https://github.com/exanauts/ExaModels.jl) [@shin2023accelerating], numerical integration from SciML's [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs) [@rackauckas2017differentialequations], and visualization through [Plots.jl](https://docs.juliaplots.org) [@PlotsJL]. @@ -54,7 +54,7 @@ OptimalControl.jl is, to our knowledge, the only Julia package that unifies both This unified approach addresses a gap in the current optimal control software landscape. Existing tools are fragmented across programming languages and paradigms. Legacy packages such as [HamPath](https://gitlab.inria.fr/ct/hampath) [@caillau2012differential], [NutoPy](https://ct.gitlabpages.inria.fr/nutopy) [@CAILLAU202213], and [COTCOT](https://github.com/mctao-inria/cotcot) [@bonnard2007second] implement sophisticated indirect methods but rely on Fortran implementations with MATLAB or Python interfaces, leading to complex and less extensible workflows. Proprietary solvers like [GPOPS-II](https://gpops2.com) [@Patterson2014] limit transparency and reproducibility. Open-source tools such as [BOCOP](https://github.com/control-toolbox/bocop) [@Bonnans2017], [ACADO](https://acado.github.io) [@Houska2011], and [acados](https://docs.acados.org) [@Verschueren2021] provide valuable direct method implementations but are not natively integrated into a modern, high-level scientific computing ecosystem. Python-based tools such as [Dymos](https://openmdao.github.io/dymos) [@Falck2021], [Pyomo.DAE](https://pyomo.readthedocs.io/en/stable/modeling_extensions/dae.html) [@Nicholson2018], [do-mpc](https://www.do-mpc.com) [@Fiedler2023], and [GEKKO](https://gekko.readthedocs.io) [@Beal2018] offer complementary capabilities but are similarly limited to direct transcription approaches within the Python ecosystem. -Within Julia, most existing packages target specific domains: [RobustAndOptimalControl.jl](https://juliacontrol.github.io/RobustAndOptimalControl.jl) for linear systems, [QuantumControl.jl](https://juliaquantumcontrol.github.io/QuantumControl.jl) and [Piccolo.jl](https://github.com/harmoniqs/Piccolo.jl) for quantum optimal control, [DirectTrajectoryOptimization.jl](https://github.com/thowell/DirectTrajectoryOptimization.jl) for trajectory problems, [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] for model predictive control, and [InfiniteOpt.jl](https://infiniteopt.github.io/InfiniteOpt.jl) [@pulsipher2022unifying] for infinite-dimensional optimization. In contrast with InfiniteOpt.jl that is designed as an extension of [JuMP.jl](https://jump.dev/JuMP.jl), our plan is to provide a modeler agnostic approach, able to accept general Julia code and leverage various optimization solvers. Besides, contributing to general-purpose NLP modeling frameworks like JuMP or [CasADi](https://web.casadi.org) [@Andersson2019] would not address the specific needs of optimal control: these tools lack native support for shooting methods based on Pontryagin's Maximum Principle and that heavily rely on differential geometric primitives. +Within Julia, most existing packages target specific domains: [RobustAndOptimalControl.jl](https://juliacontrol.github.io/RobustAndOptimalControl.jl) for linear systems, [QuantumControl.jl](https://juliaquantumcontrol.github.io/QuantumControl.jl) and [Piccolo.jl](https://github.com/harmoniqs/Piccolo.jl) for quantum optimal control, [DirectTrajectoryOptimization.jl](https://github.com/thowell/DirectTrajectoryOptimization.jl) for trajectory problems, [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] for model predictive control, and [InfiniteOpt.jl](https://infiniteopt.github.io/InfiniteOpt.jl) [@pulsipher2022unifying] for infinite-dimensional optimization. In contrast with InfiniteOpt.jl that is designed as an extension of [JuMP.jl](https://jump.dev/JuMP.jl), our package provides a modeler-agnostic approach, accepting general Julia code and leveraging various optimization solvers. Besides, contributing to general-purpose NLP modeling frameworks like JuMP or [CasADi](https://web.casadi.org) [@Andersson2019] would not address the specific needs of optimal control: these tools lack native support for shooting methods based on Pontryagin's Maximum Principle and that heavily rely on differential geometric primitives. OptimalControl.jl fills this gap by providing a DSL that matches mathematical notation, multiple discretization schemes and shooting methods, with planned support for homotopy continuation methods. The modeler-solver separation enables complementary use with InfiniteOpt.jl (JuMP-based) through alternative NLP modeling backends (currently ADNLPModels, ExaModels) and solvers. GPU acceleration and an ecosystem with domain-specific applications, tutorials, and benchmarking tools complete the offering. Target users include researchers and engineers working in optimal control, control theorists developing new algorithms, and students learning optimal control through interactive tutorials. @@ -62,11 +62,11 @@ OptimalControl.jl fills this gap by providing a DSL that matches mathematical no OptimalControl.jl requires Julia version 1.10 or later and is registered in the Julia General registry, enabling straightforward installation via `Pkg.add("OptimalControl")`. We compare it below with existing software. -- **Legacy tools (COTCOT, HamPath, NutoPy)**: These Fortran packages excel at indirect methods and homotopy continuation but require multi-language setup (Fortran plus Matlab / Python). OptimalControl.jl provides both direct and indirect methods in pure Julia with straightforward installation via package manager. +- **Legacy tools (COTCOT, HamPath, NutoPy)**: These Fortran packages excel at indirect methods and homotopy continuation but require multi-language setup (Fortran plus MATLAB / Python). OptimalControl.jl provides both direct and indirect methods in pure Julia with straightforward installation via package manager. - **Direct method tools (BOCOP, ACADO, GPOPS-II, acados, nosnoc)**: Strong direct method implementations: [GPOPS-II](https://gpops2.com) [@Patterson2014] delivers mature methods with MATLAB and C++ implementations but is proprietary; [acados](https://docs.acados.org) [@Verschueren2021] targets real-time MPC on embedded systems; [nosnoc](https://github.com/nosnoc/nosnoc) [@Nurkanovic2022] specializes in nonsmooth optimal control; [CasADi](https://web.casadi.org) [@Andersson2019], used as symbolic backend by several of these tools, is a general NLP modeler rather than an optimal control solver. OptimalControl.jl offers an open-source alternative with expressive DSL, native Julia ecosystem integration, GPU support, and unified direct and indirect approaches. -- **Julia packages**: RobustAndOptimalControl.jl targets linear systems; QuantumControl.jl, Piccolo.jl and DirectTrajectoryOptimization.jl serve specific domains; [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] focus on model predictive control. InfiniteOpt.jl addresses a very rich range of problems, including optimization on PDE's or with chance constraints, focusing on direct transcription methods. OptimalControl.jl works seamlessly on both CPU and GPU, and adds tools to do shooting in a unified framework plus systematic benchmarking through OptimalControlProblems.jl and CTBenchmarks.jl. +- **Julia packages**: RobustAndOptimalControl.jl targets linear systems; QuantumControl.jl, Piccolo.jl and DirectTrajectoryOptimization.jl serve specific domains; [LinearMPC.jl](https://darnstrom.github.io/LinearMPC.jl/stable/) [@arnstrom2022daqp] and [ModelPredictiveControl.jl](https://juliacontrol.github.io/ModelPredictiveControl.jl/stable/) [@Gagnon_ModelPredictiveControl_jl_advanced_process_2024] focus on model predictive control. InfiniteOpt.jl addresses a very rich range of problems, including optimization on PDE's or with chance constraints, focusing on direct transcription methods. OptimalControl.jl supports both CPU and GPU execution (currently NVIDIA-only, via ExaModels.jl + MadNLP.jl), and adds tools to do shooting in a unified framework plus systematic benchmarking through OptimalControlProblems.jl and CTBenchmarks.jl. # Illustrative Example @@ -92,7 +92,7 @@ The package architecture balances expressiveness, performance, and extensibility 1. **DSL vs. programmatic API**: We prioritized a mathematical DSL to reduce cognitive load for domain experts, accepting increased parsing complexity handled internally. Currently we do not address optimization of PDE or stochastic systems. -2. **GPU acceleration strategy**: The modeler-solver separation enables seamless CPU-to-GPU transition. Users simply select the appropriate modeler-solver pair: ExaModels with MadNLP and the CUDSS linear solver for GPU execution. This modular approach minimizes maintenance burden while enabling GPU performance without reimplementing transcription logic. As for now, GPU support is limited to the ExaModels + MadNLP modeler-solver combination. +2. **GPU acceleration strategy**: The modeler-solver separation enables a straightforward CPU-to-GPU transition. Users select the ExaModels modeler with MadNLP and the CUDSS linear solver for GPU execution, or simply append the `:gpu` token to the `solve` call. This modular approach minimizes maintenance burden while enabling GPU performance without reimplementing transcription logic. GPU support is currently limited to NVIDIA hardware and to the ExaModels + MadNLP modeler-solver combination. 3. **Method coverage**: Supporting both direct and indirect approaches increases code complexity but serves distinct user needs: direct methods for constrained problems with many variables, indirect methods for theoretical analysis and smaller problems requiring high accuracy. Both approaches resort to iterative solvers and may converge or not, *e.g.* depending on the initial guess. In the case of optimization solvers, the full output status of the solver is returned allowing *a posteriori* analysis. @@ -104,13 +104,13 @@ Research by close collaborators further demonstrates the package's versatility a The [control-toolbox organization](https://control-toolbox.org) hosts domain-specific application packages built on OptimalControl.jl: medical imaging optimization ([MagneticResonanceImaging.jl](https://control-toolbox.org/MagneticResonanceImaging.jl)), gene regulatory networks ([PWLdynamics.jl](https://agustinyabo.github.io/PWLdynamics.jl)), spacecraft orbital transfers ([Kepler.jl](https://control-toolbox.org/Kepler.jl)), epidemiological modeling ([SIRcontrol.jl](https://anasxbouali.github.io/SIRcontrol.jl)), and variational calculus ([CalculusOfVariations.jl](https://control-toolbox.org/CalculusOfVariations.jl)). -The package serves educational purposes through [Tutorials.jl](https://control-toolbox.org/Tutorials.jl) covering topics from linear-quadratic regulators to Model Predictive Control. These resources are used in academic courses and workshops. [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) provides standardized test problems formulated in both OptimalControl DSL and JuMP, enabling systematic performance comparisons through [CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl). +The package serves educational purposes through [Tutorials.jl](https://control-toolbox.org/Tutorials.jl) covering topics from linear-quadratic regulators to Model Predictive Control. These resources are used in academic courses and workshops; the package was notably presented at JuliaCon 2023 [@caillau2023juliacon], with the documentation serving as the presentation support. [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) provides standardized test problems formulated in both OptimalControl DSL and JuMP, enabling systematic performance comparisons through [CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl). Development involves international collaborations with CNES (French space agency), Thales Alenia Space, Inria, and CNRS. The package development began in September 2022, with the first public release in February 2023. As of March 2026, OptimalControl.jl has published more than 40 releases with contributions from multiple developers across the control-toolbox ecosystem packages, demonstrating sustained community engagement. # AI Usage Disclosure -The core software implementation, algorithms, and architectural design of OptimalControl.jl were developed by the authors. Generative AI has been used to assist with code refactoring and generation of unit and integration tests. This paper was drafted by the authors and subsequently revised with AI assistance for restructuring according to JOSS format requirements and language editing. All technical content, examples, and claims reflect the authors' work and judgment. +The core software implementation, algorithms, and architectural design of OptimalControl.jl were developed by the authors. Generative AI tools—specifically Claude Sonnet (version 4.6) and Claude Opus (version 4.8) by Anthropic—have been used to assist with code refactoring and generation of unit and integration tests, always under human review. This paper was drafted by the authors and subsequently revised with AI assistance for restructuring according to JOSS format requirements and language editing. All technical content, examples, and claims reflect the authors' work and judgment. # Acknowledgements From c228d386944703b2e53a646d44f0268f42bed0ad Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Thu, 11 Jun 2026 15:48:40 +0000 Subject: [PATCH 19/29] chore: update paper.pdf --- joss/paper.pdf | Bin 262672 -> 264424 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/joss/paper.pdf b/joss/paper.pdf index 73882ea39d47dd15f7ff3ff2d6c4ab928fd9f5ad..02c5d7df688506e7d5a9d12cb657e1000a25de62 100644 GIT binary patch delta 76976 zcmV(?K-a&Jgb?VF5U?Q&0y8+5fc60tf9*ZVj$^rz_xcL`fM_nk4M-%Q%2XQTTaO!< zgW*#RJaeeB;knH3PcXOz`4&A%<;FCS=u)S|$2Ay?J^18F;(!11U-UB%Cl_&3ysD5ye;`V$@PiPA3x2NnL8!tzLKd(bpTkFfZcX`(&m@+? z*Zf_5eLVv}+86zLHpZlH_{_Teoce7~(r7dS_6~35d%%yYHNdBFUUf*dO)I@p>6wZl zO_z6{rW0CKT}rml0>LEB2}JZ#*#SxxaI?(}C8f7Jx&?0+M6^(Qve02@fBo9z?dFcO z!$Yh>(|UJ~EoggwV45P9V?)(Ny`K5Y742Qk7bDdoKC6E%O&RuE4p7JVW*~&3yMM 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b/joss/paper.bib @@ -1,7 +1,7 @@ @misc{caillau2023juliacon, author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph and Martinon, Pierre and Sed, Sophia}, - title = {{OptimalControl.jl}: a {Julia} package to model and solve optimal control problems}, + title = {On solving optimal control problems with Julia}, year = {2023}, howpublished = {JuliaCon 2023, Cambridge, MA. Talk and abstract: \url{https://pretalx.com/juliacon2023/talk/HDC8F7/}. Video recording: \url{https://www.youtube.com/watch?v=RYUtVnzLj5k}} } From 819d6e79e4f11fc72285a8d7555811432f982285 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 11 Jun 2026 17:55:42 +0200 Subject: [PATCH 21/29] joss: remove ExaModels/MadNLP names from Summary GPU clause Per citation convention, package names with references first appear in the following paragraph; the Summary now only states the NVIDIA hardware constraint without repeating the package names. --- joss/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index bdcaa469..fcabf73f 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -44,7 +44,7 @@ archive_doi: 10.5281/zenodo.13336563 [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) [@OptimalControl_jl] is a Julia [@Bezanson2017] package for modeling and solving optimal control problems governed by ordinary differential equations (ODEs). As the core of the [control-toolbox ecosystem](https://control-toolbox.org), it provides a unified framework that supports both direct and indirect solution methods with applications spanning aerospace, medical imaging, epidemiology, and quantum control. -The package features an expressive domain-specific language (DSL) built around the `@def` macro, enabling users to define control problems using notation that closely resembles standard mathematical formulations. Problems are solved through direct transcription, converting the continuous problem into a nonlinear program (NLP) using discretization schemes including Euler, trapezoidal, midpoint, and high-order Gauss-Legendre collocation. Alternatively, indirect shooting methods based on Pontryagin's Maximum Principle can be employed. The architecture relies on a modeler-solver separation that provides a modular and extensible foundation, enabling GPU execution (currently on NVIDIA hardware via ExaModels.jl and MadNLP.jl) with minimal user intervention alongside standard CPU solvers. +The package features an expressive domain-specific language (DSL) built around the `@def` macro, enabling users to define control problems using notation that closely resembles standard mathematical formulations. Problems are solved through direct transcription, converting the continuous problem into a nonlinear program (NLP) using discretization schemes including Euler, trapezoidal, midpoint, and high-order Gauss-Legendre collocation. Alternatively, indirect shooting methods based on Pontryagin's Maximum Principle can be employed. The architecture relies on a modeler-solver separation that provides a modular and extensible foundation, enabling GPU execution (currently limited to NVIDIA hardware) with minimal user intervention alongside standard CPU solvers. The ecosystem includes extensive [tutorial resources](https://control-toolbox.org/Tutorials.jl), a benchmark problem collection ([OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) [@OptimalControlProblems_jl] with formulations in OptimalControl DSL and [JuMP](https://jump.dev/JuMP.jl) [@Lubin2023]), and performance comparison tools ([CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl)). Integration with Julia's ecosystem enables access to state-of-the-art tools: NLP solvers [IPOPT](https://coin-or.github.io/Ipopt) [@Wachter2006] and [MadNLP.jl](https://github.com/MadNLP/MadNLP.jl) [@SHIN2024110651; @SHIN2021693], automatic differentiation and NLP modeling through JuliaSmoothOptimizers' [ADNLPModels](https://jso.dev/ADNLPModels.jl) [@ADNLPModels_jl], GPU acceleration via [ExaModels.jl](https://github.com/exanauts/ExaModels.jl) [@shin2023accelerating], numerical integration from SciML's [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs) [@rackauckas2017differentialequations], and visualization through [Plots.jl](https://docs.juliaplots.org) [@PlotsJL]. 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z@$L_++|vUcco;gj{{6KlH+0`1YK8ur!#Ir$vWEDs^NK>1W7fXn-+=KS`Ud1l7~d)) z<;e9)MSB<>F)_i(-okeHhwI;h8~6>UpO#;HfVND@RWgN8pSo!*BWA?!+f6@=zUr6d z2i+wP@Ot#yX}Wy9qlhpG3SNzpY0p2#lGp@73M4OG9G~5O(LGriEJo&Z#7TL=#3MLb zn@$Wc35S|=vbSfbbDiK{oTmc7FiFl$#2S7$- z2%*>NaeBo|4-8m_+U`0buBF9k#?=Z72a__*q}OuuZMK%80$Y!krk}ycMLp>I4P5Tm zI|3^A?yUkP!Bxf?H0RLx=XX4P7)Gy%vF7kZ70>KI^ho7kx``Z|#L7WR_dvsN?GB68^GUAd8XM#Q$?_ pPIN@ju>aO9ziZpS9Wy?GOiQ>-i-?3EtdSOIYlxwt>&YJ>e*x{ABYXe= From 594c63f8a92590da5e4678c59e5ea810abc91cac Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 11 Jun 2026 18:02:23 +0200 Subject: [PATCH 23/29] joss: remove "documentation as presentation support" from JuliaCon sentence --- joss/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/joss/paper.md b/joss/paper.md index fcabf73f..adb833f2 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -104,7 +104,7 @@ Research by close collaborators further demonstrates the package's versatility a The [control-toolbox organization](https://control-toolbox.org) hosts domain-specific application packages built on OptimalControl.jl: medical imaging optimization ([MagneticResonanceImaging.jl](https://control-toolbox.org/MagneticResonanceImaging.jl)), gene regulatory networks ([PWLdynamics.jl](https://agustinyabo.github.io/PWLdynamics.jl)), spacecraft orbital transfers ([Kepler.jl](https://control-toolbox.org/Kepler.jl)), epidemiological modeling ([SIRcontrol.jl](https://anasxbouali.github.io/SIRcontrol.jl)), and variational calculus ([CalculusOfVariations.jl](https://control-toolbox.org/CalculusOfVariations.jl)). -The package serves educational purposes through [Tutorials.jl](https://control-toolbox.org/Tutorials.jl) covering topics from linear-quadratic regulators to Model Predictive Control. These resources are used in academic courses and workshops; the package was notably presented at JuliaCon 2023 [@caillau2023juliacon], with the documentation serving as the presentation support. [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) provides standardized test problems formulated in both OptimalControl DSL and JuMP, enabling systematic performance comparisons through [CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl). +The package serves educational purposes through [Tutorials.jl](https://control-toolbox.org/Tutorials.jl) covering topics from linear-quadratic regulators to Model Predictive Control. These resources are used in academic courses and workshops; the package was notably presented at JuliaCon 2023 [@caillau2023juliacon]. [OptimalControlProblems.jl](https://control-toolbox.org/OptimalControlProblems.jl) provides standardized test problems formulated in both OptimalControl DSL and JuMP, enabling systematic performance comparisons through [CTBenchmarks.jl](https://control-toolbox.org/CTBenchmarks.jl). Development involves international collaborations with CNES (French space agency), Thales Alenia Space, Inria, and CNRS. The package development began in September 2022, with the first public release in February 2023. As of March 2026, OptimalControl.jl has published more than 40 releases with contributions from multiple developers across the control-toolbox ecosystem packages, demonstrating sustained community engagement. 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a/joss/paper.bib +++ b/joss/paper.bib @@ -24,6 +24,7 @@ @article{rackauckas2017differentialequations number={1}, pages={15}, year={2017}, + doi={10.5281/zenodo.591257}, publisher={Ubiquity Press} } @@ -40,6 +41,7 @@ @software{ADNLPModels_jl license = {MPL-2.0}, title = {{ADNLPModels.jl: Automatic Differentiation models implementing the NLPModels API}}, url = {https://github.com/JuliaSmoothOptimizers/ADNLPModels.jl}, +doi = {10.5281/zenodo.4605982}, year = {2023} } @@ -208,14 +210,14 @@ @article{bonnard2007second } @article{pulsipher2022unifying, - title = {A unifying modeling abstraction for infinite-dimensional optimization}, - journal = {Computers & Chemical Engineering}, - volume = {156}, - year = {2022}, - issn = {0098-1354}, - doi = {10.1016/j.compchemeng.2021.107567}, - url = {https://www.sciencedirect.com/science/article/pii/S0098135421003458}, - author = {Pulsipher, Joshua L. and Zhang, Weiqi and Hongisto, Tyler J. and Zavala, Victor M.} + title = {A unifying modeling abstraction for infinite-dimensional optimization}, + journal = {Computers & Chemical Engineering}, + volume = {156}, + year = {2022}, + issn = {0098-1354}, + doi = {10.1016/j.compchemeng.2021.107567}, + url = {https://www.sciencedirect.com/science/article/pii/S0098135421003458}, + author = {Pulsipher, Joshua L. and Zhang, Weiqi and Hongisto, Tyler J. and Zavala, Victor M.} } @article{caillau2012differential, @@ -480,6 +482,7 @@ @software{Orban_NLPModelsIpopt_jl title = {{NLPModelsIpopt.jl: A thin IPOPT wrapper for NLPModels}}, url = {https://github.com/JuliaSmoothOptimizers/NLPModelsIpopt.jl}, version = {0.10.1}, + doi = {10.5281/zenodo.2629034}, year = {2023} } @@ -532,6 +535,7 @@ @software{Montoison_MUMPS_jl title = {{MUMPS.jl: A Julia Interface to MUMPS}}, url = {https://github.com/JuliaSmoothOptimizers/MUMPS.jl}, version = {1.4.1}, + doi={10.5281/zenodo.3271646}, year = {2024} } From e50cb6c6e62a8a605671ee19abc3f556896400c1 Mon Sep 17 00:00:00 2001 From: GitHub Actions Date: Mon, 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