Necessary Optimality Conditions for an Optimal Control Problem Governed by an Inclusion with Discontinuous Right—Hand Side

We deal with an optimal control problem of the Bolza type, where the controlled system is governed by a generalized sweeping process, which is a special differential inclusion with discontinuous right-hand side. Employing a suitable constraint qualification, we restate the problem using distance functions and use the fuzzy sum rule to obtain fuzzy optimality conditions. Furthermore, we derive pointwise optimality conditions around a local minimum and discuss the possibility of letting the fuzzy parameter converge to zero to derive optimality conditions at a local minimum. Introduction In this article we are interested in a two–level optimization problem