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Considering the attractor structure of chaotic maps for observer-based synchronization problems

Author

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  • Millerioux, G.
  • Anstett, F.
  • Bloch, G.

Abstract

The main purpose of this paper is to state some sufficient conditions for global synchronization of chaotic maps. The synchronization is viewed as a state reconstruction problem which is tackled by polytopic observers. Unlike most standard observers, polytopic observers can account for a special property of chaotic dynamics. Indeed, it is shown that many chaotic maps can be described in a so-called convexified form, involving a time-varying parameter which depends on the chaotic state vector. Such a form makes it possible to incorporate knowledge on the structure of the compact set wherein the parameter lies. This set depends implicitly on the structure of the chaotic attractor. It is proved that the conservatism of the polyquadratic stability conditions for the state reconstruction, stated in a companion paper, can be reduced when the corresponding Linear Matrix Inequalities involve the vertices of the minimal convex hull of this set. Theoretical developments along with special emphasis on computational aspects are provided and illustrated in the context of adaptive synchronization.

Suggested Citation

  • Millerioux, G. & Anstett, F. & Bloch, G., 2005. "Considering the attractor structure of chaotic maps for observer-based synchronization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(1), pages 67-85.
    • Handle: RePEc:eee:matcom:v:68:y:2005:i:1:p:67-85
    DOI: 10.1016/j.matcom.2004.10.001
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    References listed on IDEAS

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    1. Chatterjee, Sangit & Chatterjee, Samprit, 1990. "A note on finding extreme points in multivariate space," Computational Statistics & Data Analysis, Elsevier, vol. 10(1), pages 87-92, August.
    2. Daafouz, Jamal & Millerioux, Gilles, 2002. "Poly-quadratic stability and global chaos synchronization of discrete time hybrid systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 295-307.
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    Cited by:

    1. Torres, Lizeth & Besançon, Gildas & Georges, Didier & Verde, Cristina, 2012. "Exponential nonlinear observer for parametric identification and synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(5), pages 836-846.
    2. Behzad, Mehdi & Salarieh, Hassan & Alasty, Aria, 2008. "Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1295-1304.

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