juliaopt2024

Trajectory optimisation in space mechanics with Julia

Jean-Baptiste Caillau, Olivier Cots, Alesia Herasimenka

affiliations

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 (biology, space mechanics, quantum mechanics and more)
  • Additional solvers: direct shooting, collocation for BVP, Hamiltonian pathfollowing...
  • ... and open to contributions!

control-toolbox.org

control-toolbox.org

Credits (not exhaustive!)