An Adaptive Approach to Synchronization of Two Chua's Circuits
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:62706", author = "Majid Reza Naseh and Mohammad Haeri", title = "An Adaptive Approach to Synchronization of Two Chua's Circuits", 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.", volume = "1", number = "6", pages = "919-4", }
