Time optimal control for a nonholonomic system with state constraint

Jérôme Lohéac (1, 2) , Jean-François Scheid (1, 2)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECL - Institut Élie Cartan de Lorraine

The aim of this paper is to tackle the time optimal controllability of an (n+1)-dimensional nonholonomic integrator. In the optimal control problem we consider, the state variables are subject to a bound constraint. We give a full description of the optimal control and optimal trajectories are explicitly obtained. The optimal trajectories we construct, lie in a 2-dimensional plane and they are composed of arcs of circle.

Mots clés: Nonholonomic systems; Brockett integrator; time optimal control; Pontryagin's maximum principle; state constraints

Domaines: Optimisation et contrôle [math.OC]

Jérôme Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control and Related Fields, 2013, 3 (2), pp.185-208. ⟨10.3934/mcrf.2013.3.185⟩. ⟨hal-00713280v2⟩