Abstract
This paper investigates the design problem of adaptive controller and synchronizer for the Qi-Chen chaotic system (2005) with unknown parameters. First, adaptive control laws are derived to stabilize the Qi-Chen chaotic system to its unstable equilibrium at the origin. Then adaptive control laws are also derived to achieve global chaos synchronization of identical Qi-Chen chaotic systems with unknown parameters. The results derived for adaptive stabilization and synchronization for the Qi-Chen chaotic system are established using Lyapunov stability theory. Numerical simulations are presented to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper.
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References
Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)
Lakshmanan, M., Murali, K.: Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996)
Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)
Ge, S.S., Wang, C., Lee, T.H.: Adaptive backstepping control of a class of chaotic systems. Internat. J. Bifur. Chaos 10, 1149–1156 (2000)
Sun, M., Tian, L., Jiang, S., Xun, J.: Feedback control and adaptive control of the energy resource chaotic system. Chaos, Solitons & Fractals 32, 168–180 (2007)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
Lu, L., Zhang, C., Guo, Z.A.: Synchronization between two different chaotic systems with nonlinear feedback control. Chinese Physics 16(6), 1603–1607 (2007)
Sundarapandian, V.: Hybrid chaos synchronization of hyperchaotic Liu and hyperchaotic Chen systems by active nonlinear control. Internat. J. Computer Sci. Eng. Inform. Tech. 1(2), 1–14 (2011)
Liao, T.L., Tsai, S.H.: Adaptive synchronization of chaotic systems and its applications to secure communications. Chaos, Solitons & Fractals 11, 1387–1396 (2000)
Yang, T., Chua, L.O.: Control of chaos using sampled-data feedback control. Internat. J. Bifur. Chaos 9, 215–219 (1999)
Yu, Y.G., Zhang, S.C.: Adaptive backstepping synchronization of uncertain chaotic systems. Chaos, Solitons & Fractals 27, 1369–1375 (2006)
Konishi, K., Hirai, M., Kokame, H.: Sliding mode control for a class of chaotic systems. Phys. Lett. A 245, 511–517 (1998)
Sundarapandian, V.: Global chaos synchronization of Pehlivan systems by sliding mode control. Internat. J. Comp. Sci. Eng. 3(5), 2163–2169 (2011)
Qi, G., Chen, G., Du, S., Chen, Z., Yuan, Z.: Analysis of a new chaotic system. Physica A 352, 295–308 (2005)
Hahn, W.: The Stability of Motion. Springer, New York (1967)
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© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Vaidyanathan, S. (2012). Adaptive Controller and Synchronizer Design for the Qi-Chen Chaotic System. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds) Advances in Computer Science and Information Technology. Computer Science and Engineering. CCSIT 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27308-7_13
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DOI: https://doi.org/10.1007/978-3-642-27308-7_13
Publisher Name: Springer, Berlin, Heidelberg
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