Transient bounds of dynamic certainty equivalent adaptive controllers

Abstract

AbstractIn this paper we show that the transient bounds of Morse's dynamic certainty equivalent adaptive controller established previously by us can be considerably strengthened. Specifically, we derive a computable bound on the ℒ︁∞‐norm of the tracking error which, in contrast with the local bound obtained previously by us, holds for all system initial conditions. Also, we add an ‘adaptation gain’ in the high‐order estimator to prove that, by increasing this gain, the ℒ︁∞‐norm of the tracking error can be made arbitrarily small without increasing its ℒ︁∞ norm. This is an improvement over the results obtained with backstepping designs, where these performance measures must be traded off in the selection of the adaptation speed.