OUTPUT FEEDBACK MIN-MAX CONTROL PROBLEM FOR A CLASS OF UNCERTAIN LINEAR STOCHASTIC SYSTEMS ON UMD BANACH SPACE

Abstract

In this paper we consider the problem of quadratic linear min-max regulator problem on a UMD (Unconditional Martingale Differences) Banach space where the system is to be regulated by output feedback subject to measurement uncertainty. The problem is to find an optimal feedback policy (an operator valued function) that minimizes the maximum risk (or loss). We prove existence of an optimal policy, as an output feedback operator valued function, and present the necessary conditions of optimality. Also we present a convergence theorem based on the necessary conditions of optimality. The results presented here are new even in the Hilbert space setting.