A necessary optimality condition of the Pontryagin maximum principle type in one problem of optimal control of a system with distributed parameters

Abstract

We consider a variable-structure optimal control problem described in different domains by a hyperbolic integro-differential equation and a Volterra integral equation, respectively. The quality functional is terminal. A formula for the increment of the quality criterion is constructed and an analogue of L.S. Pontryagin's maximum principle is proved by investigating on special McShane-type variations.