CERTAIN NONLINEAR PARTIALLY OBSERVABLE STOCHASTIC OPTIMAL-CONTROL PROBLEMS WITH EXPLICIT CONTROL LAWS EQUIVALENT TO LEQG LQG PROBLEMS/

This paper is concerned with partially observed stochastic optimal con trol problems when nonlinearities enter the dynamics of the unobservab le state and the observations as gradients of potential functions, Exp licit representations for the information state are derived in terms o f a finite number of sufficient statistics, Consequently, the partiall y observed problem is recast as one of complete information with a new state generated by a modified version of the Kalman filter, When the terminal cost is quadratic in the unobservable state and includes the integral of the nonlinearities, the optimal control laws are explicitl y computed, similar to linear-exponential-quadratic-Gaussian and linea r-quadratic-Gaussian tracking problems, The results are applicable to filtering and control of Hamiltonian systems.