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The purpose of this paper is to establish an optimal control of nonlinear dynamical systems with state-independent noise under noisy observations. Guided by the state-space representation concept, we describe approximately mathematical models for both the dynamical systems and the observation process by the nonlinear vector stochastic differential equation of Ito-type. First, for the purpose of establishing an approximate approach. to solve state estimation problems of nonlinear stochastic systems in Markovian framework, a method of stochastic linearization is introduced which will hopefully be of anextensive use to the optimal control version. Secondly, by using the estimator dynamics obtained, an approximation to the optimal control is presented with respect to a quadratic cost functional. Finally, detailed discussions are given by a numerical example including quantitative aspects of sample paths behavior of optimal control signal and state estimation.

An Approximate Method of Optimal Control for Nonlinear Stochastic Dynamical Systems under Noisy Observations