A CLASS OF NONLINEAR EVOLUTION EQUATIONS ON BANACH SPACES DRIVEN BY FINITELY ADDITIVE MEASURES AND ITS OPTIMAL CONTROL

Abstract

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by finitely additive measures generalizing the classical models of impulsive systems. We use measures as controls and prove existence of optimal controls and present necessary (and sufficient) conditions of optimality. Further, we prove a convergence theorem based on the necessary conditions of optimality. Using the general results we construct the necessary conditions of optimality for purely impulsive systems. In the final section we extend our results from signed measures to finitely additive vector measures taking values in infinite dimensional Banach spaces.