Optimal Control of Stochastic Linear Distributed Parameter Systems

Abstract

In this article we give necessary and sufficient conditions of optimality for linear stochastic distributed parameter systems, with convex differentiable payoffs and partial observation. They are obtained through variational methods, which can be applied only in the case of fixed information (i.e., not dependent on the control or the state). However, by a density argument it is proven that an optimal control adapted to the observation is also optimal for a space of controls adapted to some fixed information. Therefore we can get the necessary and sufficient conditions also in the case of feedback controls. We then prove, as a consequence, the separation principle for distributed parameter systems in the case of a quadratic payoff.