{"title":"GPI Observer-based Tracking Control and Synchronization of Chaotic Systems","authors":"Dangjun Zhao, Yongji Wang, Lei Liu","volume":56,"journal":"International Journal of Electrical and Computer Engineering","pagesStart":815,"pagesEnd":819,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15075","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.<\/p>\r\n","references":"[1] R. C. Hilborn, Chaos and Nonlinear Dynamics: An Introduction for\r\nScientists and Engineers, New York, USA: Oxford University Press, 2000.\r\n[2] L. M. Pecora, and T. L Carroll, \"Synchronization in chaotic systems,\"\r\nPhys. Rev. A, vol. 64, pp. 821-824, 1990.\r\n[3] F. Chen, and W. Zhang, \"LMI criteria for robust chaos synchronization\r\nof a class of chatic systems,\" Nonlinear Analysis,vol. 67, pp. 3384-3393,\r\n2007.\r\n[4] A. Lor'\u2500\u2592a, E. Panteley, and Zavala-R'\u2500\u2592o, \"Adaptive Observers With Persistency\r\nof Excitation for Synchronization of Chaotic Systems,\", IEEE\r\nTransactions on Circuits and Systems I, vol. 56, no. 12, pp. 2703-2716,\r\n2009.\r\n[5] Y. W. Wang, C. Wen, M. Yang, and J. W. Xiao, \"Adaptive control\r\nand synchronization for chaotic systems with parametric uncertainties,\"\r\nPhysics Letters A, vol. 372, pp. 2409-2414, 2008.\r\n[6] S. Dadras, and H. R. Momeni, \"Control uncertain Genesio-Tesi Chaotic\r\nSystem: adaptive sliding mode approach,\", Chaos Solitons Fract., vol. 42,\r\npp. 3140-3146, 2009.\r\n[7] Z. K. Sun, W. Xu, and X. L. Yang, \"Adaptive scheme for time-varying\r\nanticipating synchronization of certain or uncertain chaotic dynamical\r\nsystems,\" Mathematical and Computer Modeling, vol. 48, pp. 1018-1032,\r\n2008.\r\n[8] C. K. Ahn, S. T. Jung, S. K. Kang, and S. C. Joo, \"Adaptive H\u221e synchronization for uncertain chaotic systems with external disturbance,\"\r\nCommun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 2168-2177, 2010.\r\n[9] C. Yin, S. M. Zhong, and W. F. Chen, \"Design PD controller for masterslave\r\nsynchronization of chaotic Lur-e system with sector and slope\r\nrestricted nonlinearities,\" Commun. Nonlinear Sci. Numer. Simulat., vol.\r\n16, pp. 1632-1639, 2011.\r\n[10] M. Fliess, and R. Marquez, \"Continuous-time linear predictive control\r\nand flatness: A module-theoretic setting with examples,\" Int. J. Control,\r\nvol. 73, pp. 606-623, 2000.\r\n[11] M. Fliess, and J. C'edric, \"Model-free control and intelligent PID\r\ncontroller: torwards a possible trivialization of nonlinear control?\", 15th\r\nIFAC Symposium on System Identification, IFAC, pp. 1-6, 2009.\r\n[12] A. Luviano-Ju'arez, J. Cort'es-Romero, and H. Sira-Ram'\u2500\u2592rez, \"Synchronization\r\nof chaotic oscilators by means of proportional integral observers,\"\r\nInternational Journal of Bifurcation and Chaos, vol. 20, pp. 1509-1517,\r\n2010.\r\n[13] H. Sira-Ramirez, V. Feliu-Batlle, F. Beltran-Carbajal, and A. Blanco-\r\nOrtega, \"Sigma-Delta modulation sliding mode observers for linear\r\nsystems subject to locally unstable inputs,\" Control and Automation,\r\n2008 16th Mediterranean Conference on, 2008.\r\n[14] Martinez-Vazquez D L, Rodriguez-Angeles A, and Sira-Ram'\u2500\u2592rez H,\r\n\"Robust GPI Observer under noisy measurements,\" 6th International Conference\r\non Electrical Engineerying, Computing Science and Automatic,\r\nToluca, Jan.10-13, pp. 1-6, 2009.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 56, 2011"}