Adaptive control using a Kalman fibre based estimation algorithm

The adaptive control of linear time-varying systems is addressed. A Kalman-filter-based estimation algorithm, which can be seen as a generalization of the least-squares algorithm, is considered. It is shown that a certainty equivalence controller leads to bounded disturbance/bounded state stability in the deterministic framework. A modified algorithm can be used to obtain identical results when unmodeled dynamics exist. Analogous results are obtained in the stochastic case. In the time-invariant case, the controlled system is guaranteed stable if the system is minimum phase