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Active sliding mode control antisynchronization of chaotic systems with uncertainties and external disturbances. (English) Zbl 1244.93109
Summary: The antisynchronization behavior of chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical chaotic systems with different initial conditions and two different chaotic systems with terms of uncertainties and external disturbances are derived based on the Lyapunov stability theory. Analysis and numerical simulations are shown for validation purposes.
MSC:
93C95 Application models in control theory
34H10 Chaos control for problems involving ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821-824, 1990. · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[2] G. Chen and X. Dong, From Chaos to Order, vol. 24 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, Singapore, 1998. · Zbl 0908.93005
[3] M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proceedings of the Royal Society of London A, vol. 458, no. 2019, pp. 563-579, 2002. · Zbl 1026.01007 · doi:10.1098/rspa.2001.0888
[4] G. Hu, Y. Zhang, H. A. Cerdeira, and S. Chen, “From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems,” Physical Review Letters, vol. 85, no. 16, pp. 3377-3380, 2000. · doi:10.1103/PhysRevLett.85.3377
[5] M. C. Ho, Y. C. Hung, and C. H. Chou, “Phase and anti-phase synchronization of two chaotic systems by using active control,” Physics Letters Section A, vol. 296, no. 1, pp. 43-48, 2002. · Zbl 1098.37529 · doi:10.1016/S0375-9601(02)00074-9
[6] A. Uchida, Y. Liu, I. Fischer, P. Davis, and T. Aida, “Chaotic antiphase dynamics and synchronization in multimode semiconductor lasers,” Physical Review A, vol. 64, no. 2, pp. 023801-023807, 2001.
[7] G.-H. Li and S.-P. Zhou, “Anti-synchronization in different chaotic systems,” Chaos, Solitons and Fractals, vol. 32, no. 2, pp. 516-520, 2007. · doi:10.1016/j.chaos.2006.05.076
[8] M. M. El-Dessoky, “Synchronization and anti-synchronization of a hyperchaotic Chen system,” Chaos, Solitons and Fractals, vol. 39, no. 4, pp. 1790-1797, 2009. · Zbl 1197.37026 · doi:10.1016/j.chaos.2007.06.053
[9] M. M. Al-Sawalha and M. S. M. Noorani, “Chaos anti-synchronization between two novel different hyperchaotic systems,” Chinese Physics Letters, vol. 25, no. 8, pp. 2743-2746, 2008. · doi:10.1088/0256-307X/25/8/003
[10] M. M. Al-sawalha and M. S. M. Noorani, “Active anti-synchronization between identical and distinctive hyperchaotic systems,” Open Systems and Information Dynamics, vol. 15, no. 4, pp. 371-382, 2008. · Zbl 1188.70060 · doi:10.1142/S1230161208000250
[11] M. Mossa Al-sawalha and M. S. M. Noorani, “On anti-synchronization of chaotic systems via nonlinear control,” Chaos, Solitons and Fractals, vol. 42, no. 1, pp. 170-179, 2009. · Zbl 1198.93145 · doi:10.1016/j.chaos.2008.11.011
[12] M. M. Al-Sawalha and M. S. M. Noorani, “Anti-synchronization of two hyperchaotic systems via nonlinear control,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3402-3411, 2009. · Zbl 1221.37210 · doi:10.1016/j.cnsns.2008.12.021
[13] M. M. Al-sawalha and M. S. M. Noorani, “Anti-synchronization of chaotic systems with uncertain parameters via adaptive control,” Physics Letters Section A, vol. 373, no. 32, pp. 2852-2857, 2009. · Zbl 1233.93056 · doi:10.1016/j.physleta.2009.06.008
[14] M. M. Al-sawalha, M. S. M. Noorani, and M. M. Al-dlalah, “Adaptive anti-synchronization of chaotic systems with fully unknown parameters,” Computers & Mathematics with Applications, vol. 59, no. 10, pp. 3234-3244, 2010. · Zbl 1222.34059 · doi:10.1016/j.cnsns.2009.11.001
[15] R. Li, W. Xu, and S. Li, “Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1288-1296, 2009. · Zbl 1197.37138 · doi:10.1016/j.chaos.2007.09.032
[16] J. Horng, H. K. Chen, and Y. K. Lin, “Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems,” Chaos, Solitons and Fractals, vol. 39, no. 2, pp. 707-716, 2009. · Zbl 1197.37003 · doi:10.1016/j.chaos.2007.01.104
[17] Q. Song and J. Cao, “Synchronization and anti-synchronization for chaotic systems,” Chaos, Solitons and Fractals, vol. 33, no. 3, pp. 929-939, 2007. · Zbl 1133.37313 · doi:10.1016/j.chaos.2006.01.041
[18] M. Zribi, N. Smaoui, and H. Salim, “Synchronization of the unified chaotic systems using a sliding mode controller,” Chaos, Solitons and Fractals, vol. 42, no. 5, pp. 3197-3209, 2009. · Zbl 1198.93024 · doi:10.1016/j.chaos.2009.04.051
[19] Y. Zhao and W. Wang, “Chaos synchronization in a Josephson junction system via active sliding mode control,” Chaos, Solitons and Fractals, vol. 41, no. 1, pp. 60-66, 2009. · Zbl 1198.34127 · doi:10.1016/j.chaos.2007.11.010
[20] E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130-141, 1963. · Zbl 1417.37129
[21] G. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 7, pp. 1465-1466, 1999. · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[22] J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, UK, 2003. · Zbl 1012.37001
[23] J. Lü, G. Chen, and S. Zhang, “Dynamical analysis of a new chaotic attractor,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 5, pp. 1001-1015, 2002. · Zbl 1044.37021 · doi:10.1142/S0218127402004851
[24] R. Genesio and A. Tesi, “Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems,” Automatica, vol. 28, no. 3, pp. 531-548, 1992. · Zbl 0765.93030 · doi:10.1016/0005-1098(92)90177-H
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