Model reference adaptive control of linear time-varying plants: the case of ‘jump’ parameter variations

In this paper we consider the model reference adaptive control problem of single-input single-output linear, time-varying plants. We assume that the plant parameters are uniformly bounded and piecewise Lipschitz continuous. Inside the intervals of continuity, we assume that the plant satisfies certain controllability, observability, relative degree and zero dynamics assumptions but the speed of parameter variations is not restricted to be small. Under these general conditions we design a control law of the model reference type which guarantees the boundedness of the closed-loop plant and small tracking error in the mean-square sense, provided that the number of discontinuities of the plant parameters is small, on average. Furthermore, in the case of partially unknown plant parameters, we show that the adaptive controller obtained by combining this control law with a suitable estimation algorithm, guarantees closed-loop boundedness and small tracking error in the mean-square sense, provided that, in addition, the functional dependence on time of the controller parameters is known up to a slowly time-varying component.