Bernoulli Variable Model for Nonlinear Systems

Chapter

Abstract

The ILC design and analysis are addressed in this chapter for stochastic nonlinear systems with random data dropouts. The data dropout is modeled by Bernoulli random variable to describe the successful transmission or loss. Both intermittent and successive update schemes are considered, where the former stops updating if no information is received, whereas the latter keeps updating based on the latest available data. It is strictly proved the almost sure convergence of both schemes.

References

  1. 1.
    Sun, M., Wang, D.: Analysis of nonlinear discrete-time systems with higher-order iterative learning control. Dyn. Control 11, 81–96 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bu, X., Yu, F., Hou, Z.-S., Wang, F.: Iterative learning control for a class of nonlinear systems with random packet losses. Nonlinear Anal.: Real World Appl. 14(1), 567–580 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Tan, Y., Dai, H.-H., Huang, D., Xu, J.-X.: Unified iterative learning control schemes for nonlinear dynamic systems with nonlinear input uncertainties. Automatica 48(12), 3173–3182 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, Y., Wen, C., Gong, Z., Sun, M.: An iterative learning controller with initial state learning. IEEE Trans. Autom. Control 44(2), 371–376 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yang S., Xu J.-X., Huang D.: Iterative learning control for multi-agent systems consensus tracking. In: Proceedings of the 51st IEEE Conference on Decision and Control, pp. 4672–4677 (2012)Google Scholar
  6. 6.
    Xu, J.-X., Yan, R.: On initial conditions in iterative learning control. IEEE Trans. Autom. Control 50(9), 1349–1354 (2005)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Chow, Y.S., Teicher, H.: Probability Theory: Independence, Interchangeability, Martingales. Springer, New York (1978)CrossRefGoogle Scholar
  8. 8.
    Wang, D.: Convergence and robustness of discrete time nonlinear systems with iterative learning control. Automatica 34(11), 1445–1448 (1998)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shen, D., Zhang, C., Xu, Y.: Intermittent and successive ILC for stochastic nonlinear systems with random data dropouts. Asian J. Control (2018).  https://doi.org/10.1002/asjc.1480CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina

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