Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm

Israr Ahmad, Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shahzad


Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical) adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive Control and Synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov Direct Method, the Adaptive Control Techniques are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive Control Law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive Controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using mathematica 9.

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S. Boccaletti, C. Grebogi, Y. C. Lai, H. Mancini, D. Moza, “The control of chaos: theory and applications”, Physics reports, vol. 329: pp. 103-197, 2000.

I. Pehlivan, Y. Uyaroglua, “A new chaotic attractor from General Lorenz system family and its electronic experimental implementation”, Turk Jour. of Elec. Eng. & Comp. Sci, vol. 18, no. 2, 2010.

E. Ott, C. Grebogi, J. A. Yorke, Controlling Chaos, Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.

K. Pyragas, V. Pyragas, I. Z. Kiss, J. L. Hudson, “Adaptive control of unknown unstable steady states of dynamical systems”, Phy. Rev. E vol. 70, 2004.

L. M. Pecora, T. L. Carroll, “Synchronization in Chaotic Systems”, Phys. Rev. Lett., vol 64, no. 8, pp. 821–825, 1990.

A. Saaban, A. Ibrahim, M. Shahzad, I. Ahmad, “Identical Synchronization of a New Chaotic System via Nonlinear Control and Linear Active Control Techniques: A Comparative Analysis”, International Journal of Hybrid Information Technology, vol. 7, no. 1, pp. 211-224, 2014.

L. O. Chua, M. Komuro, S. Tanaka, “Simplest chaotic nonautonomous circuit”, Phys. Rev. A, vol. 30, pp. 1155-1158, 1984.

I. Ahmad, A. Saaban, A. Ibrahim, M. Shahzad, “Global Chaos Synchronization of Two different Chaotic Systems Using Nonlinear Control”, International Journal of Sciences: Basic and Applied Research (IJSBAR), vol. 13, no. 1, pp. 225-238, 2014.

B. Idowu, U. Vincent, A. Njah, “Generalized Adaptive Backstepping Synchronization for Non-identical Parametrically Excited Systems”, Nonlinear Analysis: Modelling and Control, vol. 18, no. 1, pp. 112–128, 2013.

K. S Ojo, A. Njah, S. Ogunjo, “Comparison of backsteeping and modified active control in projective synchronization of chaos in an extended Bonhoffer-van der Pol Oscillator”, Pranama Journal of Physics, vol. 80, no. 5, pp 825-835, 2013.

J. Xing, “Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters”, Nonlinear Analysis: Modelling and Control, vol. 18, no. 1, pp 112–128, 2013.

S. Vaidyanathen, “Adaptive Control and Synchronization of Shimizu-Morioka Chaotic System”, International Journal in Foundations of Computer Science & Technology, vol. 2, no. 4, pp 29-42, 2012.

O. Olusola, “Adaptive Synchronization of identical and Nonidentical Hyperchaotic Systems with unknown Parameters”, The African Review of Physics, vol. 7, pp 345-352, 2012.

M. Ali Khan, “Adaptive Synchronization of two coupled Netwon-Leipnik System with Uncertain Parameter”, Int. Journal of Basic and Applied Sciences, vol. 1., no. 4, pp 439-447, 2012.

S. Vaidyanathen, K. K. Rajagopal, “Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Systems via Adaptive Control”, Int. Journal of Soft Computing, vol. 7, no. 1, pp 28-37, 2012.

H. Zhang, X. Ma, B. Xue, “A novel boundedness-based linear and nonlinear approach to control chaos”, Chaos, Solitons and Fractals, vol. 22, pp 433-442, 2004.

S. Al-Hadhrami, A. Saaban, A. Ibrahim, M. Shazad, I. Ahmad, “Linear Active Control Algorithm to Synchronize a Nonlinear HIV/AIDS Dynamical System”, Asian Journal of Applied Sciences and Engineering, vol. 3, no. 2, pp 96-115, 2014.

C. Li, L. Wu, H. Li, Y. Tong, “A novel chaotic system and its topological horseshoe”, Nonlinear Analysis, Modelling and Control, vol. 18, no. 1, pp 66–77, 2013.

H. K. Khalil, Non Linear dynamical Systems, Prentice Hall, 3rd Ed, NJ 07458, USA, 2002.

M. Aghababa, H. Aghababa, “Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties”, Nonlinear Dyn, vol. 67, pp 2689-2701, 2012.

Z. Xinghua, D. Shougang, “Adaptive Chaos Synchronization for a Type of Non-Smooth-Air-Gap Permanent Magnet Synchronous Motors”, Control and Decision Conference, 2008, Ding Shougang, China.

M. Ying-Ying, L. Yun-Gang, “Barbalat’s Lemma and its application in analysis of system stability”, Journal of Shandong University of Technology, vol. 37, no. 1, pp 51-55, 2007.

L. Nguyen, K. Hong, “Adaptive Synchronization of two coupled chaotic Hindmarsh-Rose Neurons by controlling the membrane potential of a slave neuron”, Applied Mathematical Modeling, vol. 37, no. 4, pp 2460-2468, 2013.

T. Zhou, G. Chen, “Classification of Chaos in 3-D Autonomous Quadratic System-1. Basic Framework and Method”, International Journal of Bifurcation and Chaos, vol. 16, no. 9, pp 2456-2479, 2006.



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