STOCHASTIC CONTROL PROBLEM WITH PARTIAL OBSERVATIONS

Abstract

Abstract The problem of stdchastic control with observations had been discussed. First we start with the problem of linear filtering to get the best estimate for the system according to the given observations. To obtained the solution we solve Kalman filter equation. In the case of nonlinear filtering the problem reduces to complete study of Zakai equation. The optimal stochastic control dynamic system had been discussed in the case of partial infonnation which yields Kalman filter. But in the case of complete observation we solve the problem using Hamilton-Jacobi equation. Finally we introduce and discuss some applications of the problem of stochastic control.