Synchronization of Two Identical Wang Chaotic Systems via Active Sliding Mode Control

Fayiz Abu Khadra^1,

¹Mechanical Engineering Department, King Abdulaziz University, Rabigh, Saudi Arabia

Cite this paper:
Fayiz Abu Khadra. Synchronization of Two Identical Wang Chaotic Systems via Active Sliding Mode Control. Journal of Automation and Control. 2017; 5(1):1-6. doi: 10.12691/automation-5-1-1

Abstract

This paper investigates the design of active sliding mode controllers to synchronize two identical Wang chaotic systems. The switching function matrix is determined based on linear quadratic minimization process. The stability of the controllers is established using the Lyapunov stability theory. Numerical results are shown to demonstrate the effectiveness of the proposed control method.

Keywords:
Wang chaotic systems active control sliding mode control linear quadratic minimization

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Figures

References:

[1]	D. T. Mihailović, G. Mimić, and I. Arsenić, “Climate Predictions: The Chaos and Complexity in Climate Models,” Adv. Meteorol., vol. 2014, pp. 1-14, 2014.
[2]	F. Battelli, M. Feckan, and M. Franca, “On the chaotic behavior of a compressed beam,” Dyn. PDE, vol. 4, no. 1, pp. 55-86, 2007.
[3]	I. R. Epstein and K. Showalter, “Nonlinear chemical dynamics: oscillations, patterns, and chaos,” J. Phys. Chem., vol. 100, no. 31, pp. 13132-13147, 1996.
[4]	M. Feki, “Anadaptive chaos synchronization scheme applied to secure communication,” Chaos Solitons Fractals, no. 18, pp. 141-148, 2003.
[5]	X. Tan, J. Zhang, and Y. Yang, “Synchronizing chaotic systems using backstepping design,” Chaos Solitons Fractals, vol. 16, no. 1, pp. 37-45, 2003.
[6]	A. N. Njah, “Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques,” Nonlinear Dyn., vol. 61, no. 1-2, pp. 1-9, Jul. 2010.
[7]	F. Min and A. C. J. Luo, “Sinusoidal synchronization of a Duffing oscillator with a chaotic pendulum,” Phys. Lett. A, vol. 375, no. 34, pp. 3080-3089, Aug. 2011.
[8]	X. Wu, J. Cai, and M. Wang, “Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control,” Chaos Solitons Fractals, vol. 36, no. 1, pp. 121-128, Apr. 2008.
[9]	R. Aguilar-López and R. Martı´nez-Guerra, “Control of chaotic oscillators via a class of model free active controller: Suppresion and synchronization,” Chaos Solitons Fractals, vol. 38, no. 2, pp. 531-540, Oct. 2008.
[10]	M. A. Khanesar, M. Teshnehlab, and O. Kaynak, “Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller,” Soft Comput., vol. 16, no. 7, pp. 1253-1265, Jul. 2012.
[11]	X.-T. Tran and H.-J. Kang, “A novel observer-based finite-time control method for modified function projective synchronization of uncertain chaotic (hyperchaotic) systems,” Nonlinear Dyn., vol. 80, no. 1-2, pp. 905-916, Apr. 2015.
[12]	W.-D. Chang and J.-J. Yan, “Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems,” Chaos Solitons Fractals, vol. 26, no. 1, pp. 167–175, Oct. 2005.
[13]	S. Vaidyanathan, “Adaptive Backstepping Controller and Synchronizer Design for Arneodo Chaotic System With Unknown Parameters,” Int. J. Comput. Sci. Inf. Technol., vol. 4, no. 6, pp. 143-157, Dec. 2012.
[14]	S. Xu and Y. Yang, “Generalized synchronization of coupled Duffing oscillators: an LMI based approach,” in Proceedings of the 2010 American Control Conference, 2010, pp. 1761-1766.
[15]	A. Rodríguez, J. De León, and L. Fridman, “Synchronization in reduced-order of chaotic systems via control approaches based on high-order sliding-mode observer,” Chaos Solitons Fractals, vol. 42, no. 5, pp. 3219-3233, Dec. 2009.
[16]	M. A. Khan, A. K. Mondal, and S. Poria, “Three control strategies for unified chaotic system,” Int. J. Appl. Mech. AndEngineering, vol. 16, no. 2, p. 597, 2011.
[17]	M. A. Khan, “Adaptive synchronization of two coupled Newton-Leipnik systems with uncertain parameter,” Int. J. Basic Appl. Sci., vol. 1, no. 4, pp. 439-447, 2012.
[18]	M. A. Khan and S. Poria, “Generalized Synchronization of Nuclear Spin Generator System and the Application in Secure Communication,” J. Dyn. Syst. Geom. Theor., vol. 10, no. 1, pp. 53-59, May 2012.
[19]	M. A. Khan and S. Poria, “Projective synchronization of chaotic systems with bidirectional nonlinear coupling,” Pramana, vol. 81, no. 3, pp. 395-406, Sep. 2013.
[20]	E.-W. Bai and K. E. Lonngren, “Synchronization of two Lorenz systems using active control,” Chaos Solitons Fractals, vol. 8, no. 1, pp. 51-58, 1997.
[21]	Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation. New York, NY: Springer New York, 2014.
[22]	C. Edwards and S. Spurgeon, Sliding mode control: theory and applications. CRC Press, 1998.
[23]	L. Wang, “3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system,” Nonlinear Dyn., vol. 56, no. 4, pp. 453-462, Jun. 2009.