Robust adaptive tracking control of uncertain discrete time systems

Abstract

In this paper, the problem of robust adaptive tracking for uncertain discrete-time systems is considered from the slowly varying systems point of view. The class of uncertain discrete-time systems considered is subjected to both 𝓁∞ to 𝓁∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen-time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst-case steady-state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁∞ to 𝓁∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady-state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.