Necessary Optimality Conditions for an Optimal Control Problem Governed by an Inclusion with Discontinuous Right-Hand Side
2012
Abstract
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.