MINIMAL TIME PROBLEM WITH IMPULSIVE CONTROLS

Karl Kunisch (1, 2) , Zhiping Rao (2)

1 IM - Institut für Mathematik [Graz]
2 RICAM - Johann Radon Institute for Computational and Applied Mathematics

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is estab-lished. The value functional satisfies a Hamilton-Jacobi-Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.

Mots clés: optimal control; impulsive differential equations; Hamilton-Jacobi-Bellman equations

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Karl Kunisch, Zhiping Rao. MINIMAL TIME PROBLEM WITH IMPULSIVE CONTROLS. 2015. ⟨hal-01107381⟩