On convex control problems on infinite intervals

Abstract

This paper is concerned with optimal control problems with convex cost criterion and an infinite time horizon associated with linear evolution equations in Hilbert spaces. The main result (see Theorems 1 and 2 below) show that under certain assumptions the optimal control can be synthesized via a nonlinear feehack law of subgradient type. For linear control processes with quadratic cost criterion this problem has been studied in the book of Lions [13] and in the work of Datko [8, 93, Lukes and Russel [14], and Curtain and Pritchard [7]. Our treatement of such problems differs of that used by these authors but is close to that used by the author [I, 2, 41 in the study of convex control problems on finite interval. The background material on convex analysis relevant to this paper can be found in [3, 6, 161.