Markov Chain Model for Linear Systems

Chapter

Abstract

This chapter contributes to the mean square and almost sure convergence analysis of ILC algorithms for linear systems with data dropouts. The data dropout model considered in this chapter is described by a Markov chain model. The proposed stochastic approximation-type ILC algorithm copes with unreliable communication conditions including stochastic measurement noises, random transmission gains, and Markov data dropouts. Under mild assumptions, we establish the mean square and almost sure convergence of the proposed algorithm for both conventional and general Markov chain models, using time-invariant and varying step sizes.

References

  1. 1.
    Saab, S.S.: A discrete-time stochastic learning control algorithm. IEEE Trans. Autom. Control 46(6), 877–887 (2001)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chen, H.F.: Almost sure convergence of iterative learning control for stochastic systems. Science in China (Series F) 46(1), 67–79 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Huang, S.N., Tan, K.K., Lee, T.H.: Necessary and sufficient condition for convergence of iterative learning algorithm. Automatica 38(7), 1257–1260 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Meng, D., Jia, Y., Du, J., Yu, F.: Necessary and sufficient stability condition of LTV iterative learning control systems using a 2-D approach. Asian J. Control 13(1), 25–37 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Xiao, N., Xie, L., Qiu, L.: Feedback stabilization of discrete-time networked systems over fading channels. IEEE Trans. Autom. Control 57(9), 2176–2189 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dey, S., Leong, A.S., Evans, J.S.: Kalman filtering with faded measurements. Automatica 45, 2223–2233 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Polyak, B.: Introduction to Optimization. Optimization Software Inc., New York (1987)MATHGoogle Scholar
  8. 8.
    Goodwin, G., Sin, K.: Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, N.J. (1984)MATHGoogle Scholar
  9. 9.
    Zhou, W., Yu, M., Huang, D.: A high-order internal model based iterative learning control scheme for discrete linear time-varying systems. Int. J. Autom. Comput. 12(3), 330–336 (2015)CrossRefGoogle 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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