Remarks on the explicit solutions for nonlinear partially observable stochastic control problems and relations to H∞ or robust control

Partially observable stochastic and H^∞ control problems are considered. The dynamics include nonlinearities which are the gradient of some potential function in addition to linear terms, the observations are linear, and the cost functions include quadratic functions and terms related to the nonlinearities in the dynamics. Solutions of the information states for these problems are obtained. These are the analogs of the optimal observer dynamics of linear-exponential-quadratic-Gaussian (LEQG) and linear-quadratic-H^∞ (LQH^∞) tracking problems. This enables one to convert the partially observable problems into equivalent completely observable control problems. The optimal control laws for these problems are then shown to be linear feedback equivalent to LEQG and LQH^∞ tracking problems. Relations between the two solutions are also investigated