A framework for stability analysis of high-order nonlinear systems based on the CMAC method  

作　　者：Tiantian JIANG Hongxin WU 

机构地区：[1]Science and Technology on Space Intelligent Control Laboratory,Beijing Institute of Control Engineering

出　　处：《Science China(Information Sciences)》2016年第11期29-48,共20页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 61333008);National Key Basic Research Program and Development Program of China (973) (Grant No. 2013CB733100)

摘　　要：A framework for analyzing the stability of a class of high-order minimum-phase nonlinear systems of relative degree two based on the characteristic model-based adaptive control （CMAC） method is presented. In particular, concerning the tracking problem for such high-order nonlinear systems, by introducing a consistency condition for quantitatively describing modeling errors corresponding to a group of characteristic models together with a certain kind of CMAC laws, we prove closed-loop stability and show that such controllers can make output tracking error arbitrarily small. Furthermore, following this framework, with a specific characteristic model and a golden-section adaptive controller, detailed sufficient conditions to stabilize such groups of high- order nonlinear systems are presented and, at the same time, tracking performance is analyzed. Our results provide a new perspective for exploring the stability of some high-order nonlinear plants under CMAC, and lay certain theoretical foundations for practical applications of the CMAC method.A framework for analyzing the stability of a class of high-order minimum-phase nonlinear systems of relative degree two based on the characteristic model-based adaptive control （CMAC） method is presented. In particular, concerning the tracking problem for such high-order nonlinear systems, by introducing a consistency condition for quantitatively describing modeling errors corresponding to a group of characteristic models together with a certain kind of CMAC laws, we prove closed-loop stability and show that such controllers can make output tracking error arbitrarily small. Furthermore, following this framework, with a specific characteristic model and a golden-section adaptive controller, detailed sufficient conditions to stabilize such groups of high- order nonlinear systems are presented and, at the same time, tracking performance is analyzed. Our results provide a new perspective for exploring the stability of some high-order nonlinear plants under CMAC, and lay certain theoretical foundations for practical applications of the CMAC method.

关 键 词：characteristic model characteristic model-based adaptive control （CMAC） consistency condition stability high-order nonlinear system 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]