GPI Observer-based Tracking Control and Synchronization of Chaotic Systems
Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.
[1] R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for
Scientists and Engineers, New York, USA: Oxford University Press, 2000.
[2] L. M. Pecora, and T. L Carroll, "Synchronization in chaotic systems,"
Phys. Rev. A, vol. 64, pp. 821-824, 1990.
[3] F. Chen, and W. Zhang, "LMI criteria for robust chaos synchronization
of a class of chatic systems," Nonlinear Analysis,vol. 67, pp. 3384-3393,
2007.
[4] A. Lor'─▒a, E. Panteley, and Zavala-R'─▒o, "Adaptive Observers With Persistency
of Excitation for Synchronization of Chaotic Systems,", IEEE
Transactions on Circuits and Systems I, vol. 56, no. 12, pp. 2703-2716,
2009.
[5] Y. W. Wang, C. Wen, M. Yang, and J. W. Xiao, "Adaptive control
and synchronization for chaotic systems with parametric uncertainties,"
Physics Letters A, vol. 372, pp. 2409-2414, 2008.
[6] S. Dadras, and H. R. Momeni, "Control uncertain Genesio-Tesi Chaotic
System: adaptive sliding mode approach,", Chaos Solitons Fract., vol. 42,
pp. 3140-3146, 2009.
[7] Z. K. Sun, W. Xu, and X. L. Yang, "Adaptive scheme for time-varying
anticipating synchronization of certain or uncertain chaotic dynamical
systems," Mathematical and Computer Modeling, vol. 48, pp. 1018-1032,
2008.
[8] C. K. Ahn, S. T. Jung, S. K. Kang, and S. C. Joo, "Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance,"
Commun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 2168-2177, 2010.
[9] C. Yin, S. M. Zhong, and W. F. Chen, "Design PD controller for masterslave
synchronization of chaotic Lur-e system with sector and slope
restricted nonlinearities," Commun. Nonlinear Sci. Numer. Simulat., vol.
16, pp. 1632-1639, 2011.
[10] M. Fliess, and R. Marquez, "Continuous-time linear predictive control
and flatness: A module-theoretic setting with examples," Int. J. Control,
vol. 73, pp. 606-623, 2000.
[11] M. Fliess, and J. C'edric, "Model-free control and intelligent PID
controller: torwards a possible trivialization of nonlinear control?", 15th
IFAC Symposium on System Identification, IFAC, pp. 1-6, 2009.
[12] A. Luviano-Ju'arez, J. Cort'es-Romero, and H. Sira-Ram'─▒rez, "Synchronization
of chaotic oscilators by means of proportional integral observers,"
International Journal of Bifurcation and Chaos, vol. 20, pp. 1509-1517,
2010.
[13] H. Sira-Ramirez, V. Feliu-Batlle, F. Beltran-Carbajal, and A. Blanco-
Ortega, "Sigma-Delta modulation sliding mode observers for linear
systems subject to locally unstable inputs," Control and Automation,
2008 16th Mediterranean Conference on, 2008.
[14] Martinez-Vazquez D L, Rodriguez-Angeles A, and Sira-Ram'─▒rez H,
"Robust GPI Observer under noisy measurements," 6th International Conference
on Electrical Engineerying, Computing Science and Automatic,
Toluca, Jan.10-13, pp. 1-6, 2009.
[1] R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for
Scientists and Engineers, New York, USA: Oxford University Press, 2000.
[2] L. M. Pecora, and T. L Carroll, "Synchronization in chaotic systems,"
Phys. Rev. A, vol. 64, pp. 821-824, 1990.
[3] F. Chen, and W. Zhang, "LMI criteria for robust chaos synchronization
of a class of chatic systems," Nonlinear Analysis,vol. 67, pp. 3384-3393,
2007.
[4] A. Lor'─▒a, E. Panteley, and Zavala-R'─▒o, "Adaptive Observers With Persistency
of Excitation for Synchronization of Chaotic Systems,", IEEE
Transactions on Circuits and Systems I, vol. 56, no. 12, pp. 2703-2716,
2009.
[5] Y. W. Wang, C. Wen, M. Yang, and J. W. Xiao, "Adaptive control
and synchronization for chaotic systems with parametric uncertainties,"
Physics Letters A, vol. 372, pp. 2409-2414, 2008.
[6] S. Dadras, and H. R. Momeni, "Control uncertain Genesio-Tesi Chaotic
System: adaptive sliding mode approach,", Chaos Solitons Fract., vol. 42,
pp. 3140-3146, 2009.
[7] Z. K. Sun, W. Xu, and X. L. Yang, "Adaptive scheme for time-varying
anticipating synchronization of certain or uncertain chaotic dynamical
systems," Mathematical and Computer Modeling, vol. 48, pp. 1018-1032,
2008.
[8] C. K. Ahn, S. T. Jung, S. K. Kang, and S. C. Joo, "Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance,"
Commun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 2168-2177, 2010.
[9] C. Yin, S. M. Zhong, and W. F. Chen, "Design PD controller for masterslave
synchronization of chaotic Lur-e system with sector and slope
restricted nonlinearities," Commun. Nonlinear Sci. Numer. Simulat., vol.
16, pp. 1632-1639, 2011.
[10] M. Fliess, and R. Marquez, "Continuous-time linear predictive control
and flatness: A module-theoretic setting with examples," Int. J. Control,
vol. 73, pp. 606-623, 2000.
[11] M. Fliess, and J. C'edric, "Model-free control and intelligent PID
controller: torwards a possible trivialization of nonlinear control?", 15th
IFAC Symposium on System Identification, IFAC, pp. 1-6, 2009.
[12] A. Luviano-Ju'arez, J. Cort'es-Romero, and H. Sira-Ram'─▒rez, "Synchronization
of chaotic oscilators by means of proportional integral observers,"
International Journal of Bifurcation and Chaos, vol. 20, pp. 1509-1517,
2010.
[13] H. Sira-Ramirez, V. Feliu-Batlle, F. Beltran-Carbajal, and A. Blanco-
Ortega, "Sigma-Delta modulation sliding mode observers for linear
systems subject to locally unstable inputs," Control and Automation,
2008 16th Mediterranean Conference on, 2008.
[14] Martinez-Vazquez D L, Rodriguez-Angeles A, and Sira-Ram'─▒rez H,
"Robust GPI Observer under noisy measurements," 6th International Conference
on Electrical Engineerying, Computing Science and Automatic,
Toluca, Jan.10-13, pp. 1-6, 2009.
@article{"International Journal of Information, Control and Computer Sciences:64071", author = "Dangjun Zhao and Yongji Wang and Lei Liu", title = "GPI Observer-based Tracking Control and Synchronization of Chaotic Systems", abstract = "Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.
", keywords = "GPI observer, sliding mode control, master-slave synchronization,chaotic systems.", volume = "5", number = "8", pages = "957-4", }
