Optimal control of nonconvex integro-differential sweeping processes

TL;DR

This paper introduces the first study of optimal control problems for nonconvex integro-differential sweeping processes, establishing existence of solutions and deriving necessary optimality conditions using advanced variational analysis.

Contribution

It is the first to analyze optimal control for integro-differential sweeping processes with nonconvex sets and to develop necessary optimality conditions using discrete approximation methods.

Findings

Existence of optimal solutions is proven.

Necessary optimality conditions are derived.

Applications to electrical circuit control are demonstrated.

Abstract

This paper is devoted to the study, for the first time in the literature, of optimal control problems for sweeping processes governed by integro-differential inclusions of the Volterra type with different classes of control functions acting in nonconvex moving sets, external dynamic perturbations, and integral parts of the sweeping dynamics. We establish the existence of optimal solutions and then obtain necessary optimality conditions for a broad class of local minimizers in such problems. Our approach to deriving necessary optimality conditions is based on the method of discrete approximations married to basic constructions and calculus rules of first-order and second-order variational analysis and generalized differentiation. The obtained necessary optimality conditions are expressed entirely in terms of the problem data and are illustrated by nontrivial examples that include applications to optimal control models of non-regular electrical circuits.