Finite time linear quadratic control for weakly regular linear systems

Abstract

This paper is devoted to the study of the finite time linear quadratic (LQ) control problem for weakly regular linear systems, a rather broad class of infinite dimensional linear systems with unbounded input and output operators. We show that the finite time LQ optimal control problem for weakly regular linear systems has a unique solution for every initial state. We give a formula for the optimal cost operator [prod ] (t) and show that {[prod ] (t)} is a strongly continuous family of bounded linear operators. Finally, we prove that, under certain conditions, the optimal cost operator satisfies a differential Riccati equation, as in the cases of classical bounded systems and of Pritchard–Salamon systems.