Immersion and invariance adaptive control of nonlinearly parameterized nonlinear systems

  • Authors:

  • Xiangbin Liu;Romeo Ortega;Hongye Su;Jian Chu

  • Affiliations:

  • State Key Lab. of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, P. R. China and Electronic Information Engineering College, Henan University ...;Laboratoire des Signaux et Systémes Supelec, Gif-sur-Yvette, France;State Key Lab. of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, P. R. China;State Key Lab. of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, P. R. China

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity-or the related property of convexity-have already been explored by several authors with convexity being an a priori assumption that is valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. One consequence of this fact is that the controller does not rely on state-dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.