Model Reference Adaptive Control for Nonlinear Systems with Unknown Degrees

General Case

Abstract

In most of the studies of model reference adaptive control, it is assumed that an upper bound on the degree of the controlled system is known. It makes the scope of application of model reference adaptive control too restrictive, since the reasonable upper bound on the degree cannot be specified a priori in many practical cases.
In the present paper, we propose a design method of model reference adaptive control systems for nonlinear systems with unknown degrees. The present adaptive controller is composed of high gain feedbacks of hierarchical structures derived from backstepping techniques, and the degree of it is independent of the degree of the controlled system. It is shown that the resulting control system is uniformly bounded, and that the tracking error converges to an arbitrarily small residual region. Finally, several simulation studies also show the effectiveness of the proposed method.