A characterization of ε-optimal controls for stochastic systems with partial observations via the unnormalized conditional density

Abstract

Abstract The paper considers optimal control for continuous-time stochastic systems with noisy measurements of the state. It is known that the optimum coat for this problem may not be achieved within the class of strict-sense controls. However, allowing for tolerances of size e, a characterization is given for e-optimal controls in terms of a semigroup formulation involving the unnormalized conditional density of the distribution of the state, given the observations.