[1]LIU Zhen,TAN Xiangmin,YI Jianqiang,et al.Immersion and invariance theory and its application in nonlinear adaptive control[J].CAAI Transactions on Intelligent Systems,2013,8(5):400-407.[doi:10.3969/j.issn.1673-4785.201212012]
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Immersion and invariance theory and its application in nonlinear adaptive control

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 8 Number of periods: 2013 5 Page number: 400-407 Column: 综述 Public date: 2013-10-25
Title:
Immersion and invariance theory and its application in nonlinear adaptive control
Author(s):
LIU Zhen;  TAN Xiangmin;  YI Jianqiang;  YUAN Ruyi;  FAN Guoliang
Integrated Information System Research Center, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
Keywords:
nonlinear control;  immersion and invariance theory;  adaptive control;  control law;  unknown point mass system
CLC:
TP273
DOI:
10.3969/j.issn.1673-4785.201212012
Abstract:
The actual engineering demands and the complexities of the nonlinear system theory have led it to become the most attractive and challenging research field in control subjects, therefore, a new nonlinear control law design method—immersion and invariance (I&I) theory has been introduced. With this method, a (partially) asymptotically stable system with a dimension less than that of the controlled system is firstly selected as the target system, then the immersion mapping and control law are designed to make the controlled dynamics of the original system is an immersion image of the target system. In addition, the control law can keep the image of the target system as an invariant and attractive manifold, and render the trajectory of the closed-loop system bounded. Focusing on the unknown point mass model, a new nonlinear immersion and invariance adaptive control law is designed for realizing the precise tracking of a reference command. Compared with the adaptive control law based on the certainty-equivalent principle, the simulation results show that the proposed I&I adaptive control law is quite effective for processing a system with unknown parameters.
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