Filtering Method for Linear and Non-Linear Stochastic Optimal Control Of Partially Observable Systems

This paper studies two linear methods for linear and non-linear stochastic optimal control of partially observable problem (SOCPP). At first, it introduces the general form of a SOCPP and states it as a functional matrix. A SOCPP has a payoff function which should be minimized. It also has two dynamic processes: state and observation. In this study, it is presented a deterministic method to find the control factor which has named feedback control and stated a modified complete proof of control optimality in a general SOCPP. After finding the optimal control factor, it should be substituted in the state process to make the partially observable system. Next, it introduces a linear filtering method to solve the related partially observable system with complete details. Finally, it is presented a heuristic method in discrete form for estimating non-linear SOCPPs and it is stated some examples to evaluate the performance of introducing methods.