Asymptotic optimal control of a switching diffusion with small observation noise

This paper deals with nonlinear filtering and control of a switching diffusion coupled by an unknown Markov chain. A statistical estimation method is used to track the unknown Markov chain. Computable approximate filters are obtained based on this method. The filters are then used to construct controls for the partially observed system. These controls are shown to be asymptotically optimal as the observation noise tends to zero. Finally, an example is considered and numerical experiments are reported