Optimal Output Feedback Control Law for a Class of Uncertain Infinite Dimensional Dynamic Systems
In this paper we consider a class of partially observed semilinear dynamic systems on infinite dimensional Banach spaces subject to measurement uncertainty. The problem is to find an output feedback control law, an operator valued function, that minimizes the maximum risk. We present a result on the existence of an optimal (output feedback) operator valued function in the presence of uncertainty. We also present necessary conditions of optimality for feedback control laws from the space of operator valued functions endowed with the Tychonoff product topology. Based on the necessary conditions, we propose an algorithm whereby one can construct the optimal output feedback law. The results are illustrated by some examples on linear quadratic control problems.