Optimal feedback control law for some stochastic integrodifferential equations on Hilbert spaces

In this work, we consider a class of partially observed stochastic integrodifferential equations on Hilbert spaces subject to measurement uncertainty. We prove the existence of optimal feedback control law from a class of operator valued functions furnished with the product topology. This work is an extension of [2] for uncertain systems governed by stochastic differential equations on Hilbert spaces ; whereby the measurement uncertainty is a square integrable stochastic process. We illustrate the abstract results proved by analyzing an example.