Performance Bounds for Morse's Dynamic Certainty Equivalence Adaptive Controllert

In this paper we consider a model reference adaptive control scheme where the classical error augmentation and standard tuning error normalirat.ion are avoided through the use of Morse's high order tuner. We consider the particular scheme of Morse where the concept of dynamic certainty equivalence is used to reduce the error equation to one that involves only first order dynamics. With such an error equation. it is first shown that one can directly obtain computable Lz ond L , bonnds on the tracking error. This is an improvement over some earlier results where either only local L , bounds were obtained or the calculation of the global bounds required additional computation. Second. inserting an adaptive gain into Morse's high order tuner, we show that fast adaptation improves both the Lz and L, bounds on the tracking error. in the sense that the effect of the parametric uncertainty on these bounds is attenuated. Finally. using a simple example we demonstrate how an earlier attempt to use the adaptive gain to simultaneously attenuate the effect of the parametric uncertainty well as the initial conditions on the L2 bound lor the tracking error has led to an incorrect result.