Minimum switching control for adaptive tracking

The switching control approach has attracted a lot of attention recently for solving adaptive control problems. This approach relies on the condition that there exist a finite (or countable) number of non-switching controllers such that at least one of them will be able to control a given family of unknown (uncertain) plants. In this paper, we consider a class of minimum-phase plants (MIMO) with some mild closedness assumptions. Given any polynomial reference input, we provide a switching control law which guarantees the 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 non-switching controllers required for switching. In particular, the number is equal to 2 for a single-input single-output plant (one for each sign of the high-frequency gain), and is equal to 2^m for an m-input m output plant. In particular, the number is independent of the degree and the relative degree of the plant