Random Sequence Model for Linear Systems

  • Dong Shen


The random sequence model is formulated in this chapter. The intermittent update scheme is proposed for linear systems and its almost sure convergence analysis is given. The extension to systems with arbitrary relative degree is addressed and the mean square convergence for the intermittent update scheme is also established.


  1. 1.
    Chen, H.F., Guo, L.: Identification and Stochastic Adaptive Control. Birkh\(\ddot{\rm a}\)user Boston (1991)Google Scholar
  2. 2.
    Chen, H.F.: Stochastic Approximation and Its Applications. Kluwer (2002)Google Scholar
  3. 3.
    Saab, S.S.: A discrete-time stochastic learning control algorithm. IEEE Trans. Autom. Control 46(6), 877–887 (2001)MathSciNetCrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Saab, S.S.: Selection of the learning gain matrix of an iterative learning control algorithm in presence of measurement noise. IEEE Trans. Autom. Control 50(11), 1761–1774 (2005)MathSciNetCrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Sun, M., Wang, D.: Initial shift issues on discrete-time iterative learning control with system relative degree. IEEE Trans. Autom. Control 48(1), 144–148 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shen, D., Wang, Y.: Iterative learning control for networked stochastic systems with random packet losses. Int. J. Control 88(5), 959–968 (2015)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Shen, D., Xu, J.-X.: A framework of iterative learning control under random data dropouts: mean square and almost sure convergence. Int. J. Adap. Control Signal Process. 31(12), 1825–1852 (2017)MathSciNetCrossRefGoogle 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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