The issue of transients in leakage-based model reference adaptive control of switched linear systems

Abstract

The literature has proven that attaining good transient behavior in leakage-based robust adaptive control of uncertain switched systems is intrinsically challenging. In fact, because the gains of the inactive subsystems must exponentially vanish during inactive times as an effect of leakage action, new learning transients will repeatedly arise at each switching instant. In this paper, a new leakage-based mechanism is designed for robust adaptive control of uncertain switched systems: in contrast to the available designs, the key innovation of the proposed one is that the adaptive gains of the inactive subsystems can be kept constant to their switched-off values, thus preventing vanishing gains. Bounded stability of the closed-loop switched system is guaranteed thanks to the introduction of an auxiliary gain playing the role of leakage. A benchmark example commonly adopted in adaptive switched literature shows that the proposed strategy can consistently improve the transient behavior under various families of switching signals.