Monotone numerical schemes and feedback construction for hybrid control systems

Roberto Ferretti (1) , Hasnaa Zidani (2, 3)

1 Dipartimento di Matematica [Roma TRE]
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
3 OC - Optimisation et commande

Hybrid systems are a general framework which can model a large class of control systems arising whenever a collection of continuous and discrete dynamics are put together in a single model. In this paper, we study the convergence of monotone numerical approximations of value functions associated to control problems governed by hybrid systems. We discuss also the feedback reconstruction and derive a convergence result for the approximate feedback control law. Some numerical examples are given to show the robustness of the monotone approximation schemes.

Mots clés: Hybrid systems; approximation of the value function; optimal feedback law

Domaines: Optimisation et contrôle [math.OC]

Roberto Ferretti, Hasnaa Zidani. Monotone numerical schemes and feedback construction for hybrid control systems. Journal of Optimization Theory and Applications, 2015, 165 (2), pp.507-531. ⟨10.1007/s10957-014-0637-0⟩. ⟨hal-00989492v2⟩