A switching adaptive controller for feedback linearizable systems

One of the main problems in applying adaptive control techniques to nonlinear systems is the problem where-although the actual plant is controllable-the identification model loses its controllability due to insufficient rich signals, large initial estimation errors, etc. Particularly in feedback linearizable systems this phenomenon occurs in the case where, although the so-called decoupling matrix of the actual plant is invertible and thus the system is fully controllable and feedback linearizable, the estimated decoupling matrix becomes noninvertible and thus the certainty-equivalent control law cannot be applied. In this paper, we propose a switching adaptive scheme which is capable of overcoming such a problem. The key idea of the proposed scheme is that it uses an adaptive high-gain derivative feedback controller whenever the certainty-equivalent feedback-linearization controller becomes nonimplementable.