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.
Presented by the member of Editorial Board:B. T. Polyak
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
\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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547207039}
Linking options:
https://www.mathnet.ru/eng/at1018
https://www.mathnet.ru/eng/at/y2007/i7/p74
This publication is cited in the following 8 articles:
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
Li-lian Huang, Lei Lin, “Parameter Identification and Synchronization of Uncertain Chaotic Systems Based on Sliding Mode Observer”, Mathematical Problems in Engineering, 2013 (2013), 1
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
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
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
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
Autom. Remote Control, 72:9 (2011), 1967–1980
Fradkov A.L., Andrievsky B., Evans R.J., “Synchronization of nonlinear systems under information constraints”, Chaos, 18:3 (2008), 037109