On the model reference adaptive control of time-varying plants

In this paper we study the problem of developing an adaptive control law which can force the output of a linear time-varying plant to track the output of a stable linear time-invariant reference model and at the same time guarantee the internal stability of the closed-loop plant. We use the new model reference controller structure, proposed in [1], that guarantees stability and zero tracking error for a general class of linear time-varying plants with known parameters and design an adaptive law to estimate the controller parameters. We show that the assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori. Such information can be incorporated in the adaptive law so that stability and tracking performance is considerably improved for a wide class of linear time-varying plants which includes plants with fast varying parameters.