Open Access Open Access  Restricted Access Subscription or Fee Access

Sliding Mode Control Based Global Chaos Synchronization of Four-Scroll Attractors

Dr. V. Sundarapandian, S. Sivaperumal

Abstract


Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the global chaos synchronization of identical Liu-Chen four-scroll chaotic attractors (2004) and identical Wang four-scroll chaotic attractors (2009). The stability results for the synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Liu-Chen four-scroll chaotic attractors and identical Wang four-scroll chaotic attractors. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper

Keywords


Global Chaos Synchronization, Chaos, Sliding Mode Control, Liu-Chen Four-Scroll Systems, Wang Four-Scroll Systems

Full Text:

PDF

References


K.T. Alligood, T. Sauer and J.A. Yorke, Chaos: An Introduction to Dynamical Systems, New York: Springer-Verlag, 1997.

L.M. Pecora and T.L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Letters, vol. 64, pp. 821-824, 1990.

M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization, Singapore: World Scientific, 1996.

S.K. Han, C. Kerrer and Y. Kuramoto, “Dephasing and bursting in coupled neural oscillators,” Phys. Rev. Letters, vol. 75, pp. 3190-3193, 1995.

B. Blasius, A. Huppert and L. Stone, “Complex dynamics and phase synchronization in spatially extended ecological system,” Nature, vol. 399, pp. 354-359, 1999.

K.M. Cuomo and A.V. Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Physical Review Letters, vol. 71, pp. 65-68, 1993.

L. Kocarev and U. Parlitz, “General approach for chaotic synchronization with applications to communication,” Physical Review Letters, vol. 74, pp. 5028-5030, 1995.

K. Murali and M. Lakshmanan, “Secure communication using a compound signal using sampled-data feedback,” Applied Mathematics and Mechanics, vol. 11, pp. 1309-1315, 2003.

E. Ott, C. Grebogi and J.A. Yorke, “Controlling chaos,” Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.

M.C. Ho and Y.C. Hung, “Synchronization of two different chaotic systems using generalized active network,” Physics Letters A, vol. 301, pp. 424-428, 2002.

L. Huang, R. Feng and M. Wang, “Synchronization of chaotic systems via nonlinear control,” Physical Letters A, vol. 320, pp. 271-275, 2004.

H.K. Chen, “Global chaos synchronization of new chaotic systems via nonlinear control,” Chaos, Solitons and Fractals, vol. 23, pp. 1245-1251, 2005.

J. Lu, X. Wu, X. Han and J. Lü, “Adaptive feedback synchronization of a unified chaotic system,” Physics Letters A, vol. 329, pp. 327-333, 2004.

S.H. Chen and J. Lü, “Synchronization of an uncertain unified system via adaptive control,” Chaos, Solitons and Fractals, vol. 14, pp. 643-647, 2002.

J.H. Park and O.M. Kwon, “A novel criterion for delayed feedback control of time-delay chaotic systems,” Chaos, Solitons and Fractals, vol. 17, pp. 709-716, 2003.

X. Wu and J. Lü, “Parameter identification and backstepping control of uncertain Lü system,” Chaos, Solitons and Fractals, vol. 18, pp. 721-729, 2003.

K. Murali and M. Lakshmanan, “Secure communication using a compound signal using sampled-data feedback,” Applied Mathematics and Mechanics, vol. 11, pp. 1309-1315, 2003.

J.E. Slotine and S.S. Sastry, “Tracking control of nonlinear systems using sliding surface with application to robotic manipulators,” Internat. J. Control, vol. 38, pp. 465-492, 1983.

V.I. Utkin, “Sliding mode control design principles and applications to electric drives,” IEEE Transactions on Industrial Electronics, vol. 40, pp. 23-36, 1993.

R. Saravanakumar, K. Vinoth Kumar and K.K. Ray, “Sliding mode control of induction motor using simulation approach,” Internat. J.Control of Computer Science and Network Security, vol. 9, pp. 93-104, 2009.

W. Liu and G. Chen, “Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor?” Internat. J. Bifurcat. Chaos, vol. 14, pp. 1395-1403, 2004.

L. Wang, “3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system,” Nonlinear Dynamics, vol. 56, pp. 453-462, 2009.

W. Hahn, The Stability of Motion, Berlin: Springer-Verlag, 1967.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.