Adaptive Control of Linear Time-Varying Plants

Abstract

In this paper we consider the model reference adaptive control (MRAC) problem of a class of linear time-varying (LTV) plants. The plant parameters are assumed to be smooth, bounded functions of time which satisfy the usual assumptions of MRAC for time-invariant plants, at each frozen time instant. We first show that if the plant parameters are sufficiently slowly-varying with time, a control parameter vector with smooth elements exists, such that the closed loop plant behaves almost like a linear time invariant reference model. We then use the robust adaptive law proposed in Ioannou and Tsakalis (1985) to adjust the controller parameters and establish boundedness for all signals in the adaptive loop for any bounded initial conditions. The bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero.