On Morse´s new adaptive controller: parameter convergence and transient performance

Some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by A.S. Morse (Proc. US-Italy Joint Seminar Syst., Models Feedback 1992). It is proved that the L₂ norm of the tracking error is uniformly bounded by the initial parameter estimation error. Further, if the initial conditions are sufficiently small, it is shown that the L_∞ norm of the tracking error is uniformly bounded by the L_m2 norm of the reference signal. These transient bounds are independent of the signals richness and the adaptation gain, making them arguably the strongest transient results available in the literature. Second, excitation conditions for exponential stability, a property which is well known to insure some local performance measures, are given. To this end, it is shown that, modulo a signal dependent time scale change, Morse´s estimator is equivalent to a normalized gradient plus filtering identifier