The viability kernel of dynamical systems with mixed constraints: A level-set approach

Abstract

This paper deals with control systems with mixed (state-control) constraints and dynamics in discrete-time. We aim at providing a practical method for computing the viability kernel for such systems. We take a standard approach via optimal control theory, that is, we identify the viability kernel as the effective domain of the value function of a suitable optimal control problem. A dynamic programming principle can be established in order to compute that value function. However, from a practical point of view this may turn out in a slow scheme for such computation, because at each step the mixed constraints need to be verified. In this work we take a different path which has been inspired by the level-set approach studied for optimal control problems with (pure) state constraints. An algorithm is proposed for computing the viability kernel and some numerical examples are shown to demonstrate the proposed method.