Bounds on achievable performance in the identification and adaptive control of time-varying systems

This paper treats the identiication and adaptive control of time-varying linear systems. For linear systems with a Gauss-Markov parameter process a global lower bound on the mean square error is obtained which is valid for any causal parameter estimator. A similar lower bound is obtained for any causal, one step ahead predictor. These bounds are applied to the adaptive control of time-varying systems to obtain a lower bound on closed loop mean square performance for any causal control law. For a speciic control law, mean square stability is established, and through simulations it is seen that the performance nearly meets the theoretical lower bound.