A CLASS OF NONSTANDARD PARTIALLY OBSERVED STOCHASTIC SYSTEMS ON A HILBERT SPACE AND THEIR OPTIMAL STRUCTURAL FEEDBACK CONTROL

摘要

In this paper we consider the question of weak compactness of the set of attainable measures on a Hilbert space induced by a class of partially observed nonstandard stochastic systems. The system is perturbed not only by Brownian motion but also by an arbitrary second order random process taking values from a Hilbert space. Structural controls used are measures with values from the space of bounded linear operators, L(Y, X) where X, Y are the state and output spaces, respectively. We consider several control problems and prove existence of optimal policies.