Minimum Switching Control for Adaptive Tracking†

The switching adaptive control method has been used for quite a few years to solve the adaptive stabilization and model reference adaptive control problems. However, a serious problem with the switching control method is that the number of “candidate” controllers can potentially be very large, especially for multi-input multi-output systems. In this paper, we consider a class of minimum-phase multi-input-multi-output plants with some mild compactness assumptions. Given any polynomial reference input, we provide a switching control law which guarantees exponentially stability of the closed-loop system with exponential tracking performance. The main contribution of the paper is that we give the minimum number of candidate controllers required for switching. In particular, the number is equal to 2 for single-input single-output plants (one for each sign of the high-frequency gain), and is equal to 2 for m-input m-output plants. That is, the number is independent of the degree and the relative degree of the plant. Copyright c © 2000 John Wiley & Sons, Ltd.