一类不确定非线性系统无过参数自适应控制设计新方法

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

文中研究了一类控制系数未知的更一般高阶不确定非线性系统的全局稳定自适应控制设计问题.尽管现有文献已解决了该问题,但对于n维系统,现有构造稳定自适应控制的方法至少需要设计n+1个未知参数的动态调节律,即动态补偿器的维数至少为n+1,存在较为严重的过参数问题.文中通过定义新的需动态调节的未知参数,运用增加幂积分和有关自适应技术,成功地解决了已有方法中的过参数问题,给出了构造只含有一个参数调节律的稳定自适应控制设计新方法.仿真算例验证了文中所给方法的有效性.

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.