Adaptive Dual Control of Discrete-Time Lqg Problems with Unknown-But-Bounded Parameter

The dual control for a class of discrete-time linear-quadratic Gaussian (LQG) problems is studied in this paper, where there exist unknown-but-bounded parameter uncertainties both in the state equation and the observation equation. It is assumed that the unknown parameter belongs to a known bounded interval. To achieve the adaptive dual control, a subdivision for the continuous bounded interval is used, thus, the computational tractability is ensured. Based on such subdivision, the adaptive dual controller developed can learn a more accurate interval that contains the true value of the unknown parameter with a learning error given in advance. The performance of the controller is illustrated with two examples.