A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients. Although the existing literature has solved the problem, for n-dimensional systems, the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller; that is, the dimension of the dynamic compensator is not less than n + 1, and therefore, there exists serious overparametrization. In this paper, by defining some new unknown parameters which need dynamic updating, also by using adding a power integrator and related adaptive technique, the overparametrization is successfully solved and a new approach is given to design stabilizing adaptive controller based on only one parameter updating law. A simulation example is finally provided to demonstrate the validness of the proposed approach.