Existence and Uniqueness of the Optimal Control in Hilbert Spaces for a Class of Linear Systems

Abstract

One analyzes the existence and uniqueness of the optimal control in the class of exactly controllable linear systems. The cases under consideration refer to the minimization of time, energy and final variety in transfer problems. The spaces of state variables X and control variables U, respectively, are Hilbert spaces. The linear operator T(t) which defines the solution of the linear control system is a strong semi group. The present analysis resorts to the results of the theory of linear operators and functional analysis.