Optimal control of systems governed by B-evolutions.

Abstract

In this thesis the question of optimal control of systems governed by B-evolutions is considered. First, a necessary conditions of optimality for a Lagrange problem subject to a semilinear systems is derived. Two cases are carried out: In the first case the Frechet differentiability of the cost integrand with respect to the control variable is assumed and in the second only the continuity. Then these results are applied to a linear quadratic regulator problem. Two results are presented one of which contains control cost and the other does not. The optimal control law is given by the solution of an appropriate operator Riccati differential equations. Finally, using the calculus of variation a result is proved on the existence of optimal controls.