Robust stability and performance improvement of discrete-time multivariable adaptive control systems

Abstract

A procedure for designing and analysing robust adaptive one-step-ahead minimum prediction error control schemes for discrete-time multivariable plants is given. A general robust adaptive law (GRAL) is developed for adjusting the controller parameters so that the closed-loop plant is globally stable despite the presence of modelling errors, and the tracking error is of the order of the modelling error in the mean. Modified adaptive laws which employ the dead-zone, the σ−, the ε₁− or the switching σ-modification proposed in the single-input, single-output continuous-time case are extended to the multivariable discrete-time case and shown to be special cases of the GRAL. As in the continuous-time case, we show that the convergence and the tracking performance of these globally stable adaptive control schemes can be considerably improved if the reference signal is chosen to be dominantly rich. Dominantly rich signals maintain a high level of persistence of excitation relative to the level of the modelling error. This guarantees exponential convergence and bounds for the tracking and parameter error, in the steady state that are of the order of the modelling error.