|
| 1 | +```@raw html |
| 2 | +<img width="800" alt="juliaopt2024" src="./assets/zhejiang-2025.jpg"> |
| 3 | +``` |
| 4 | + |
| 5 | +# Solving optimal control problems in Julia: the OptimalControl.jl package |
| 6 | + |
| 7 | +### [Jean-Baptiste Caillau](http://caillau.perso.math.cnrs.fr), [Olivier Cots](https://ocots.github.io), [Joseph Gergaud](https://github.com/joseph-gergaud), [Pierre Martinon](https://github.com/PierreMartinon), [Sophia Sed](https://sed-sam-blog.gitlabpages.inria.fr) |
| 8 | + |
| 9 | +```@raw html |
| 10 | +<img width="800" alt="affiliations" src="./assets/affil.jpg"> |
| 11 | +``` |
| 12 | + |
| 13 | +## What it's about |
| 14 | + |
| 15 | +- Nonlinear optimal control of ODEs: |
| 16 | + |
| 17 | +```math |
| 18 | +g(x(t_0),x(t_f)) + \int_{t_0}^{t_f} f^0(x(t), u(t))\, \mathrm{d}t \to \min |
| 19 | +``` |
| 20 | + |
| 21 | +subject to |
| 22 | + |
| 23 | +```math |
| 24 | +\dot{x}(t) = f(x(t), u(t)),\quad t \in [t_0, t_f] |
| 25 | +``` |
| 26 | + |
| 27 | +plus boundary, control and state constraints |
| 28 | + |
| 29 | +- Our core interests: numerical & geometrical methods in control, applications |
| 30 | + |
| 31 | +## OptimalControl.jl for trajectory optimisation |
| 32 | + |
| 33 | +- [Basic example](tutorial-double-integrator-energy.html) |
| 34 | +- [Goddard problem](tutorial-goddard.html) |
| 35 | +- [Orbit transfer](https://control-toolbox.org/Kepler.jl) |
| 36 | + |
| 37 | +## Wrap up |
| 38 | + |
| 39 | +- High level modelling of optimal control problems |
| 40 | +- Efficient numerical resolution coupling direct and indirect methods |
| 41 | +- Collection of examples |
| 42 | + |
| 43 | +## Future |
| 44 | + |
| 45 | +- New applications (pace mechanics, biology, quantum mechanics and more) |
| 46 | +- Additional solvers: optimisation on GPU, direct shooting, collocation for BVP, Hamiltonian pathfollowing... |
| 47 | +- ... and open to contributions! If you like the package, please give us a star ⭐️ |
| 48 | + |
| 49 | +```@raw html |
| 50 | +<a href="https://github.com/control-toolbox/OptimalControl.jl"><img width="800" alt="OptimalControl.jl" src="./assets/star.jpg"></a> |
| 51 | +``` |
| 52 | + |
| 53 | +## control-toolbox.org |
| 54 | + |
| 55 | +- Open toolbox |
| 56 | +- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) |
| 57 | + |
| 58 | +```@raw html |
| 59 | +<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a> |
| 60 | +``` |
| 61 | + |
| 62 | +## Credits (not exhaustive!) |
| 63 | + |
| 64 | +- [ADNLPModels.jl](https://jso.dev/ADNLPModels.jl) |
| 65 | +- [DifferentiationInterface.jl](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable) |
| 66 | +- [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl) |
| 67 | +- [Ipopt.jl](https://github.com/jump-dev/Ipopt.jl) |
| 68 | +- [MadNLP.jl](https://github.com/MadNLP/MadNLP.jl) |
| 69 | +- [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl) |
| 70 | + |
| 71 | +## Stand up for science 2025 |
| 72 | + |
| 73 | +```@raw html |
| 74 | +<a href="https://standupforscience2025.org"><img width="200" alt="stand up for science 2025" src="./assets/standup.jpg"></a> |
| 75 | +``` |
| 76 | + |
| 77 | +## Acknowledgements |
| 78 | + |
| 79 | +Jean-Baptiste Caillau is partially funded by a **France 2030** support managed by the *Agence Nationale de la Recherche*, under the reference ANR-23-PEIA-0004 ([PDE-AI](https://pde-ai.math.cnrs.fr) project). |
| 80 | + |
| 81 | +```@raw html |
| 82 | +<img width="150" alt="affiliations" src="./assets/france-2030.png"> |
| 83 | +``` |
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