A new adaptive LQG control algorithm

A new control algorithm is developed for the discrete time, finite horizon adaptive LQG problem. In the new algorithm, randomization over linear control functions is performed at future stages to find a deterministic desired control U(k) at the current stage. This randomized linear control policy, which is U(k)-dependent and non-linear in measurements, incorporates explicitly the knowledge available about the unknown parameter at future stages in terms of the posterior distribution. At the same time it enables us to obtain a closed form expression of an approximation of the optimal control-cost function. Numerical examples comparing the new solution with the optimal are also provided.