Fundamental Solutions and Optimal Control of Neutral Systems

Abstract

Abstract. In this work, we shall consider standard optimal control problems for a class of neutral functional differential equations in Banach spaces. As the basis of a systematic theory of neutral models, the fundamental solution is constructed and a variation of constants formula of mild solutions is established. Necessary conditions in terms of the solutions of neutral adjoint systems are established to deal with the fixed time integral convex cost problem of optimality. Based on optimality conditions, the maximum principle for time varying control domain is presented.