Adaptive control of linear time-varying plants

In this paper the model reference adaptive control (MRAC) problem of a class of linear time-varying (LTV) plants is considered. 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. It is first shown 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. The robust adaptive law proposed in Ioannou and Tsakalis (1986) IEEE Trans. Aut. Control, AC-31, 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions. It is shown that 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.