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CEF Techniques for Parameterized Nonlinear Continuous-Time Systems

  • Dong ShenEmail author
  • Xuefang Li
Chapter

Abstract

This chapter proposes adaptive iterative learning control (ILC) schemes for continuous-time parametric nonlinear systems with iteration lengths that randomly vary. As opposed to the existing ILC works that feature nonuniform trial lengths, this chapter is applicable to nonlinear systems that do not satisfy the globally Lipschitz continuous condition. In addition, this chapter introduces a novel composite energy function (CEF) based on newly defined virtual tracking error information for proving the asymptotical convergence. Both an original update algorithm and a projection-based update algorithm for estimating the unknown parameters are proposed. Extensions to cases with unknown input gains, iteration-varying tracking references, high-order nonlinear systems, and multi-input-multi-output systems are all elaborated upon. Illustrative simulations are provided to verify the theoretical results.

References

  1. 1.
    Xu JX, Jin X, Huang D (2014) Composite energy function-based iterative learning control for systems with nonparametric uncertainties. Int J Adapt Control Signal Process 28(1):1–13MathSciNetCrossRefGoogle Scholar
  2. 2.
    Li X, Huang D, Chu B, Xu JX (2016) Robust iterative learning control for systems with norm-bounded uncertainties. Int J Robust Nonlinear Control 26(4):697–718MathSciNetCrossRefGoogle Scholar
  3. 3.
    Shen D, Xu JX.: Adaptive learning control for nonlinear systems with randomly varying iteration lengths. IEEE Trans Neural Netw Learn Syst (2018).  https://doi.org/10.1109/TNNLS.2018.2861216

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK

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