CEF Techniques for Nonparameterized Nonlinear Continuous-Time Systems

  • Dong ShenEmail author
  • Xuefang Li


This chapter proposes robust iterative learning control schemes for continuous-time nonlinear systems with various nonparametric uncertainties under nonuniform trial length circumstances. The nonuniform trial length is described by a random variable, which causes a random data missing problem while designing and analyzing algorithms for the precise tracking problem. Three common types of nonparametric uncertainties are taken into account: norm-bounded uncertainty, variation-norm-bounded uncertainty, and norm-bounded uncertainty with unknown coefficients. A novel composite energy function is introduced with the help of a newly defined virtual tracking error for the asymptotical convergence of the proposed schemes. Extensions to multi-input-multi-output cases are also elaborated. Illustrative simulations are provided to verify the theoretical results.


  1. 1.
    Wei J, Hu Y, Sun M (2014) Adaptive iterative learning control for a class of nonlinear time-varying systems with unknown delays and input dead-zone. IEEE/CAA J Autom Sin 1(3):302–314CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Shen D, Xu JX (2018) Robust learning control for nonlinear systems with nonparametric uncertainties and nonuniform trial lengths. Int J Robust Nonlinear Control.

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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