ct: control toolbox - Numerical tools and examples in optimal control

Jean-Baptiste Caillau (1, 2) , Olivier Cots (3) , Pierre Martinon (4)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 McTAO - Mathematics for Control, Transport and Applications
3 IRIT-APO - Algorithmes Parallèles et Optimisation
4 CaGE - Control And GEometry

Combining direct and indirect methods to have the best of both worlds is an efficient method to solve numerically optimal control problems. A direct solver will typically provide information on the structure of the optimal control, allowing an educated guess for shooting. The control toolbox ct offers such possibilities and is presented on two examples. The first example has a bang-singular solution and is solved by chaining direct and indirect solvers. The second one consists in computing conjugate and cut loci on an ellipsoid of revolution, which is performed using a more advanced combination of indirect methods with differential continuation.

Keywords: direct transcription method; shooting; bocop; nutopy; differential continuation; automatic differentiation

Domains: Optimization and Control [math.OC]

Jean-Baptiste Caillau, Olivier Cots, Pierre Martinon. ct: control toolbox - Numerical tools and examples in optimal control. 2022. ⟨hal-03558975v1⟩