Directly computable L2 and Lx performance bounds for Morse's dynamic certainty equivalence adaptive controller

Abstract

In this paper we consider a model reference adaptive control scheme where the classical error augmentation and standard tuning error normalization 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 L2 and Lx bounds on the tracking error. This is an improvement over some earlier results where either only local Lx 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 L2 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 as well as the initial conditions on the L2 bound for the tracking error has led to an incorrect result.