Optimal Control of the Minimal Time Crisis Problem Type by Non-Smooth Analysis Tools

Abstract

In this work, we study an optimal control problem where theb cost functional to be minimized represents the so-called time of crisis, i.e. the time spent by a trajectory solution of a control system outside a given set K. This functional can be expressed using the characteristic function of K that is discontinuous preventing. This method uses non-smooth analysis tools and gives clearer evidence. Its also considered more general cases by including closed sets that are not necessarily convex. We provide in this paper properties of the time crisis function together with necessary optimality conditions using the Euler-Lagrange inclusion. Finally, we provide an illustrating example in which we compute explicitly an optimal feedback policy.