Limiting performance of the adaptive systems in the presence of modeling errors

In this paper we consider an adaptive controller with vanishing gain and excitation of the reference signal. We use the burst recovery concept to show that all signals in the adaptive loop remain uniformly bounded. We also show that the mean square performance converges so that the adaptive system is optimal in the sense that the parameter estimation error and the one-step ahead prediction error are uncorrelated in the mean despite the presence of the unmodelled dynamics.