×

Generalized lag-synchronization of chaotic mix-delayed systems with uncertain parameters and unknown perturbations. (English) Zbl 1203.93125

Summary: Chaotic systems in practice are always influenced by some unknown factors, which may make the chaotic behavior completely different from that of unaffected system. In this paper, the generalized lag-synchronization for a general class of coupled chaotic systems with mixed delays, uncertain parameters, as well as external perturbations is investigated. A simple but all-powerful robust adaptive controller is designed to achieve this goal. Based on Lyapunov stability theory, integral inequality and Barbalat’s lemma, rigorous proofs are given for the asymptotic stability of the error systems of the coupled systems with or without external perturbations. Sufficient conditions for inaccuracy or accuracy estimation of unknown parameters are also given. Moreover, the designed adaptive controller has better anti-interference capacity than those of references. Numerical simulations verify the effectiveness of the theoretical results.

MSC:

93C73 Perturbations in control/observation systems
93E10 Estimation and detection in stochastic control theory
62H10 Multivariate distribution of statistics
34H10 Chaos control for problems involving ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Pecora, L.; Carroll, T., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[2] Sorrentio, F.; Ott, E., Adaptive synchronization of dynamics on evolving complex networks, Phys. Rev. Lett., 100, 114101-114104 (2008)
[3] Chopra, N.; Spong, M. K., On exponential synchronization of Kuramoto oscillators, IEEE Trans. Automat. Control, 54, 2, 353-357 (2009) · Zbl 1367.34076
[4] Budini, A. A.; Cáceres, M. O., Adiabatic small noise fluctuations around anticipated synchronization: a perspective from scalar master-slave dynamics, Physica A, 387, 4483-4496 (2008)
[5] Sundar, S.; Minai, A., Synchronization of randomly multiplexed chaotic systems with application to communication, Phys. Rev. Lett., 85, 5456-5459 (2000)
[6] Bowong, S.; Moukam Kakmeni, F. M.; Fotsin, H., A new adaptive observer-based synchronization scheme for private communication, Phys. Lett. A, 355, 193-201 (2006)
[7] Shahverdiev, E. M.; Sivaprakasam, S.; Shore, K. A., Lag-synchronization in time-delayed systems, Phys. Lett. A, 292, 320-324 (2002) · Zbl 0979.37022
[8] Budini, Adrián A.; Cáceres, Manuel O., Adiabatic small noise fluctuations around anticipated synchronization: a perspective from scalar master-slave dynamics, Physica A, 387, 18, 4483-4496 (2008)
[9] Huang, Y.; Hwang, C.; Liao, T., Generalized pejective synchronization of chaotic systems with unknown dead-zone input: observer-based approach, Chaos, 16, 033125 (2006) · Zbl 1146.93368
[10] Fabricio, A.; Zhao, L.; Marcos, G.; Elbert, E., Chaotic phase synchronization and desynchronization in an oscillator network for object selection, Neural Netw., 22, 5-6, 728-737 (2009)
[11] Rulkov, N.; Sushchik, M.; Tsimring, L.; Abarbanel, H., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51, 980-994 (1995)
[12] Kocarev, L.; Parlitz, U., Generalized synchronization, predictability and equivalence of unidirectionally coupled systems, Phys. Rev. Lett., 76, 11, 1816-1819 (1996)
[13] Abarbanel, H.; Rulkov, N.; Sushchik, M., Generalized synchronization of chaos: the auxiliary system approach, Phys. Rev. E, 53, 4528-4535 (1996)
[14] Meng, J.; Wang, X., Generalized synchronization via nonlinear control, Chaos, 18, 023108 (2008) · Zbl 1307.34079
[15] He, W.; Cao, J., Generalized synchronizaton of chaotic systems: an auxiliary system approach via matrix measure, Chaos, 19, 013118 (2009) · Zbl 1311.34113
[16] Ge, Z.; Chang, C., Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function, Chaos Solitons Fractals, 39, 1959-1974 (2009) · Zbl 1197.37134
[17] Yu, Y.; Li, H., Adaptive generalized function projective synchronization of uncertain chaotic systems, Nonlinear Anal. RWA (2009)
[18] Senthilkumar, D.; Lakshmanan, M.; Kurths, J., Transition from phase to generalized synchronization in time-delay systems, Chaos, 18, 023118 (2008)
[19] Li, R., Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control, Commun. Nonlinear Sci. Numer. Simul., 14, 2757-2764 (2009) · Zbl 1221.93244
[20] Shahverdiev, E.; Sivaprakasam, S.; Shore, K., Lag-synchronization in time-delayed systems, Phys. Lett. A, 292, 320-324 (2002) · Zbl 0979.37022
[21] Li, C.; Liao, X.; Wong, K., Chaotic lag-synchronization of coupled time-delayed systems and its applications in secure communication, Physica D, 194, 187-202 (2004) · Zbl 1059.93118
[22] Huang, Y.; Wang, Y.; Xiao, J., Generalized lag-synchronization of continuous chaotic system, Chaos Solitons Fractals, 40, 766-770 (2009) · Zbl 1197.37030
[23] Lin, J.; Liao, T.; Yan, J.; Yau, H., Synchronization of unidirectional coupled chaotic systems with unknown channel time-delay: adaptive robust observer-based approach, Chaos Solitons Fractals, 26, 971-987 (2005) · Zbl 1093.93535
[24] Song, Q., Synchronization analysis of coupled connected neural networks with mixed delays, Neurocomputing, 72, 16-18, 3907-3914 (2009)
[25] Gu, K. Q.; Kharitonov, V. L.; Chen, J., Stability of Time-Delay System (2003), Birkhäuser: Birkhäuser Boston, MA
[26] Popov, V., Hyperstability of Control System (1973), Springer-Verlag: Springer-Verlag Berlin
[27] Chen, M.; Chen, W., Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems, Chaos Solitons Fractals, 41, 2716-2724 (2009) · Zbl 1198.93155
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.