Performance of adaptive predictors for Gaussian time-varying systems

This paper treats adaptive prediction for time-varying system models. For linear systems with a Gauss-Markov parameter process, a global lower bound on the mean square prediction error is obtained which is valid for any causal predictor. This requires minimal assumptions on the regressor sequence. The prediction error bound is 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. The stability of the closed loop control system, established in an earlier paper, ensures that it is possible to invoke the prediction error bound in bounding closed loop performance. Results from simulation experiments are provided to verify the tightness of these bounds