Necessary Optimality Conditions for the Time of Crisis Control Problem
Résumé
We consider a non-smooth optimal control problem where the cost functional represents the time of crisis, that is, the time spent by a solution of a control system outside a given set. A regularization scheme of the problem based on the Moreau-Yosida approximation is proposed. We prove the convergence of an optimal sequence for the approximated problem to an optimal solution of the original one. We derive optimality conditions on the original and regularized problem