Stochastic Optimal Control of a Descriptor System

Abstract

We study the optimal control problem for a descriptor system whose evolution is described by Ito’s differential-algebraic equation. The quadratic cost functional is considered. The main constraint is that the characteristic matrix pencil corresponding to the equation is regular. We establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The results are illustrated on an example of a descriptor system that describes transient states in a radio engineering filter with random perturbations in the form of white noise.