Optimal structural feedback control for partially observed stochastic systems on Hilbert space

In this paper we consider a class of structural feedback controls for partially observed stochastic systems on Hilbert space. The structural controls are measures with values from the space of bounded linear operators, L(Y,X)L(Y,X) where X,YX,Y are the state and output spaces respectively. The system is perturbed not only by Brownian motion but also by an arbitrary second order random process taking values from the Hilbert space YY. The structural control interacts with the output and the state as well as the noise in a bilinear fashion. We prove the existence of optimal policies.