An Adaptive Approach to Synchronization of Two Chua's Circuits

Authors: Majid Reza Naseh, Mohammad Haeri

Abstract:

This paper introduces an adaptive control scheme to synchronize two identical Chua's systems. Introductory part of the paper is presented in the first part of the paper and then in the second part, a new theorem is proposed based on which an adaptive control scheme is developed to synchronize two identical modified Chua's circuit. Finally, numerical simulations are included to verify the effectiveness of the proposed control method.

Keywords: Chaos synchronization, adaptive control, Chua's circuits.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081601

References:

[1] B.R .Andrievskii, A.L. Fradkov, "Control of chaos: methods and applications". Automation and Remote Control, vol. 65, no. 4, 2004, pp. 505-533.
[2] M.T. Yassen, "Adaptive control and synchronization of a modified Chua circuit system", Applied Mathematics and Computation, vol. 135, 2003, pp. 113-128.
[3] K. Pyragas, "Continuous control of chaos by self-controlling feedback", Phys. Lett. A 170, 1992.
[4] U. Dressler, G. Nitsche, "Controlling chaos using time delay coordinates", Phys. Rev. Lett , vol. 68, no. 1 ,1992.
[5] C. Wu, T. Yang, and L.O. Chua, "On adaptive synchronization and control of nonlinear dynamical Systems", Int. J. Bifurcation Chaos, vol. 6, no. 3, 1996, pp. 455-472.
[6] C.W. Wu and L.O. Chua, "A unified framework for synchronization and control of dynamical systems", Int. J. Bifurcation Chaos, vol. 4, no. 4, 1994, pp. 979-998.
[7] M.D. Bernardo, "An adaptive approach to the control and synchronization of continuous-time chaotic Systems", Int. J. Bifurcation Chaos, vol. 6, no. 3, 1996, pp.557-568.
[8] L.M. Pecora and T.L. Carroll, "Synchronization in chaotic circuits", Phys. Rev. Lett., vol. 64, no. 8, 1990, pp. 821-824.
[9] L.M Pecora and T.L. Carroll, "Driving systems with chaotic signal", Phys. Rev. A, vol. 44, no. 4, 1991, pp. 2374-2378.
[10] S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancini, and D. Maza, "The Control of Chaos: Theory and Application", Physics Reports, vol. 329, 2000, pp. 103-197.
[11] J. Sun and Y. Zhang, "Impulsive control and synchronization of Chua oscillators", Mathematics and Computers in Simulation, vol. 66, 2004, pp. 499-508.
[12] X.X. Liao, G. Chen and H.O. Wang, "On global synchronization of chaotic systems", Proc. Amer. Contr. Conf., Anchorange, Alaska, USA, vol. 8, no. 10, 2002, pp.2255-2259.
[13] X.X. Liao, Mathematical Theory and Application of Stability, Huazhong Normal University Press, China, 2001.