Optimal Control of Semilinear Unbounded Evolution Inclusions with Functional Constraints

Document Type

Article

Publication Date

12-1-2015

Abstract

This paper is devoted to the study of a Mayer-type optimal control problem for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces subject to endpoint constraints described by finitely many Lipschitzian equalities and inequalities. First we construct a sequence of discrete approximations to the optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for continuous-time evolution inclusions by passing to the limit from discrete approximations.

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