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 Avtomat. i Telemekh., 2007, Issue 7, Pages 74–89 (Mi at1018)

Adaptive observer-based synchronization of the nonlinear nonpassifiable systems

B. R. Andrieskya, V. O. Nikiforovb, A. L. Fradkova

a Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University of Information Technologies, Mechanics and Optics

Abstract: The general approach to synchronization of the dynamic systems on the bassis on the adaptive observer and the passification method was extended to the nonpassifiable nonlinear systems – in particular, to those whose model has the relative order higher than one. Two schemes of synchronization relying on the extended-error adaptive observers and the high-order tuning algorithms were proposed. Solution of the problem of synchronization relies on a new canonical form of the adaptive observer. The conditions for convergence of the parameter estimates to the true values in the case of no system noise were established, and also robustness of the adaptive synchronization to the bounded measurement error was proved. The feasibility of information transmission by modulation of the chaotic signal with the use of the proposed method was demonstrated by the example of the controllable Lorentz system.

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English version:
Automation and Remote Control, 2007, 68:7, 1186–1200

Bibliographic databases:

PACS: 02.30.Yy
Presented by the member of Editorial Board: Á. Ò. Ïîëÿê

Citation: B. R. Andriesky, V. O. Nikiforov, A. L. Fradkov, “Adaptive observer-based synchronization of the nonlinear nonpassifiable systems”, Avtomat. i Telemekh., 2007, no. 7, 74–89; Autom. Remote Control, 68:7 (2007), 1186–1200

Citation in format AMSBIB
\Bibitem{AndNikFra07} \by B.~R.~Andriesky, V.~O.~Nikiforov, A.~L.~Fradkov \paper Adaptive observer-based synchronization of the nonlinear nonpassifiable systems \jour Avtomat. i Telemekh. \yr 2007 \issue 7 \pages 74--89 \mathnet{http://mi.mathnet.ru/at1018} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2341647} \zmath{https://zbmath.org/?q=an:1141.93315} \transl \jour Autom. Remote Control \yr 2007 \vol 68 \issue 7 \pages 1186--1200 \crossref{https://doi.org/10.1134/S0005117907070077} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547207039} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Autom. Remote Control, 72:9 (2011), 1967–1980
2. Fradkov A.L., Andrievsky B., Evans R.J., “Synchronization of nonlinear systems under information constraints”, Chaos, 18:3 (2008), 037109
3. Loria A., Panteley E., Zavala-Rio A., “Adaptive Observers With Persistency of Excitation for Synchronization of Chaotic Systems”, IEEE Trans Circuits Syst I Regul Pap, 56:12 (2009), 2703–2716
4. Dimassi H., Loria A., “Adaptive Unknown-Input Observers-Based Synchronization of Chaotic Systems for Telecommunication”, IEEE Trans Circuits Syst I Regul Pap, 58:4 (2011), 800–812
5. Illing L., Fordyce R.F., Saunders A.M., Ormond R., “Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization”, American Journal of Physics, 80:3 (2012), 192–202
6. Illing L., Saunders A.M., Hahs D., “Multi-Parameter Identification From Scalar Time Series Generated by a Malkus-Lorenz Water Wheel”, Chaos, 22:1 (2012), 013127
7. Fradkov A.L., Andrievsky B., Pavlov A., “Information Transmission Over the Limited-Rate Communication Channel By Chaotic Signal Modulation and Non-Linear Observer”, IFAC PAPERSONLINE, 51:33 (2018), 91–96
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