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.