Model reference adaptive control for nonlinear systems with unknown degrees and with unknown relative degrees 1 or 2

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 cases. In the present paper, we propose a design method of model reference adaptive control systems for nonlinear systems with unknown degrees and with unknown relative degrees 1 or 2. Even if the degree of the controlled system varies, and even if the relative degree also varies between 1 and 2, the structure of the proposed adaptive controller does not change. 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