On chaotic observer design

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

Abstract

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
$$\sum\nolimits_{2} {:\left\{ {\begin{array}{*{20}{c}} {\dot{\tilde{x}} = f({{x}_{1}},{{{\tilde{x}}}_{2}}, \ldots ,{{{\tilde{x}}}_{n}})} \hfill \\ {y = h(\tilde{x}) = {{{\tilde{x}}}_{1}}} \hfill \\ \end{array} } \right.}$$

Keywords

Manifold 

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References

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    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

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