Time optimal control for a perturbed Brockett integrator

Jérôme Lohéac (1, 2) , Jean-Francois Scheid (3, 4)

1 LS2N - Laboratoire des Sciences du Numérique de Nantes
2 LS2N - équipe Commande - Commande
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
4 IECL - Institut Élie Cartan de Lorraine

The aim of this work is to compute time optimal controls for a perturbation of a Brockett integrator with state constraints. Brockett integrator and its perturbations appears in many applications fields. One of them described in details in this note is the swimming of microorganisms. We present some key results for a fast and robust numerical method to compute time optimal controls for the perturbation of a Brockett integrator. This numerical method is based on explicit formulae of time optimal controls for the Brockett integrator. The methodology presented in this work is applied to the time optimal control of a micro-swimmer.

Mots clés: Brockett integrator; Time optimal controllability; State constraints; Numerical resolution; Micro-swimmers

Domaines: Optimisation et contrôle [math.OC]

Jérôme Lohéac, Jean-Francois Scheid. Time optimal control for a perturbed Brockett integrator: Application to time optimal axi-symmetric micro-swimmers. Variational Methods In Imaging and Geometric Control, 18, , pp.454--472, 2017, Radon Series on Computational and Applied Mathematics, 978-3-11-043923-6. ⟨10.1515/9783110430394-015⟩. ⟨hal-01238610⟩