TY - JOUR

T1 - Adaptive observer-based synchronization of the nonlinear nonpassifiable systems

AU - Andrievskii, B. R.

AU - Nikiforov, V. O.

AU - Fradkov, A. L.

N1 - Funding Information: 1 This work was supported by the Russian Foundation for Basic Research, projects nos. 05-01-00869, 06-08-01386, and the Research Program no. 22 “Control Processes” of the Presidium of the Russian Academy of Sciences, project no. 1.8.

PY - 2007/7

Y1 - 2007/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34547207039&partnerID=8YFLogxK

U2 - 10.1134/S0005117907070077

DO - 10.1134/S0005117907070077

M3 - Article

AN - SCOPUS:34547207039

VL - 68

SP - 1186

EP - 1200

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 7

ER -