On chaotic observer design

  • Henk Nijmeijer
Part of the Communications and Control Engineering book series (CCE)


Chaos synchronization is an extremely exciting subject within the physics and communications society and deals with the remarkable observation that certain chaotic dynamic systems exhibit asymptotically identical motion under weak coupling between the systems. Mathematically, synchronization of two systems — sometimes called transmitter and receiver—can be cast in the following form. Given the single output system ∑1 on IR n defined by
$$\sum\nolimits_1 {:\left\{ \begin{array}{l} \dot x = f(x) = f({x_1},{x_2}, \ldots ,{x_n}){x_1}\\ y = h(x) = {x_1} \end{array} \right.} $$
introduce the system ∑2 as a copy of ∑1 with the first state component identical to y, that is
$$\sum\nolimits_{2} {:\left\{ {\begin{array}{*{20}{c}} {\dot{\tilde{x}} = f({{x}_{1}},{{{\tilde{x}}}_{2}}, \ldots ,{{{\tilde{x}}}_{n}})} \hfill \\ {y = h(\tilde{x}) = {{{\tilde{x}}}_{1}}} \hfill \\ \end{array} } \right.}$$


Chaotic System Slide Mode Control Chaos Synchronization Chaotic Dynamic System Chaotic Nature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    T. Kapitaniak, Controlling chaos, Academic Press, London, 1996.MATHGoogle Scholar
  2. [2]
    H. Nijmeijer and I.M.Y. Mareels, “An observer looks at chaos”, IEEE Trans. Circuits and Systems I, Vol. 44, pp. 882–890, 1997.MathSciNetCrossRefGoogle Scholar
  3. [3]
    E.J. Banning, On the dynamics of two coupled parametrically driven pendulums, PhD thesis, University of Twente, 1997.Google Scholar
  4. [4]
    J. Gauthier, H. Hammouri and S. Othman, “A simple observer for nonlinear systems, applications to bioreactors”, IEEE Trans. Automat. Contr. Vol. 37, pp. 875–880, 1992.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    H. Nijmeijer, “On synchronization of chaotic systems”, Proceedings 36th IEEE Conference on Decision and Control, San Diego, Cal., pp. 384–388, 1997.Google Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Henk Nijmeijer
    • 1
    • 2
  1. 1.Systems, Signals and Control Department, Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands
  2. 2.Faculty of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations