A linear dynamic feedback controller for stochastic systems with unknown parameters

The problem of controlling a stochastic system containing constant but unknown parameters over a finite horizon is considered. The expected value of a quadratic scalar performance index, with respect to the prior statistics of the parameters of the system, is minimized. Due to the complexity of this dual control optimization problem we propose to fix the structure of the estimator-controller and choose the feedback gain, the parameter estimates, and filter gain such that the performance index is minimized. We develop a design procedure for optimizing the constant parameters of this controller. This procedure is attractive when the horizon is short but it also incorporates adaptation to long term changes in the statistics of the plant parameters.