Solving optimal control problems in Julia: the OptimalControl.jl package
Jean-Baptiste Caillau, Olivier Cots, Joseph Gergaud, Pierre Martinon, Sophia Sed
What it's about
- Nonlinear optimal control of ODEs:
\[g(x(t_0),x(t_f)) + \int_{t_0}^{t_f} f^0(x(t), u(t))\, \mathrm{d}t \to \min\]
subject to
\[\dot{x}(t) = f(x(t), u(t)),\quad t \in [t_0, t_f]\]
plus boundary, control and state constraints
- Our core interests: numerical & geometrical methods in control, applications
OptimalControl.jl for trajectory optimisation
Wrap up
- High level modelling of optimal control problems
- Efficient numerical resolution coupling direct and indirect methods
- Collection of examples
Future
- New applications (pace mechanics, biology, quantum mechanics and more)
- Additional solvers: optimisation on GPU, direct shooting, collocation for BVP, Hamiltonian pathfollowing...
- ... and open to contributions! If you like the package, please give us a star ⭐️
control-toolbox.org
- Open toolbox
- Collection of Julia Packages rooted at OptimalControl.jl
Credits (not exhaustive!)
Stand up for science 2025
Acknowledgements
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 project).
