Adaptive LQG regulator via the separation principle

The continuous-time linear quadratic adaptive control problem with average cost per unit time is studied. It is shown that a consistent estimator of an unknown parameter and the optimal control can be obtained by using the separation principle, which decomposes the problem into two parts: to find the consistent estimator in the case without controls; and to solve the Riccati equation in the LQ regulator problem with the parameter estimate replacing the unknown parameter.<
>