A research on adaptive control to stabilize and synchronize a hyperchaotic system with uncertain parameters

Israr Ahmad, Azizan Bin Saaban, Adyda Binti Ibrahim, Said Al-Hadhrami, Mohammad Shahzad, Sharifa Hilal Al-Mahrouqi

Abstract


This paper addresses the chaos control and synchronization problems of a hyperchaotic system. It is assumed that the parameters of the hyperchaotic system are unknown and the system is perturbed by the external disturbance. Based on the Lyapunov stability theory and the adaptive control theory, suitable nonlinear controllers are designed for the asymptotic stability of the closed-loop system both for stabilization of hyperchaos at the origin and complete synchronization of two identical hyperchaotic systems. Accordingly, suitable update laws are proposed to estimate the fully uncertain parameters. All simulation results are carried out to validate the effectiveness of the theoretical findings. The effect of external disturbance is under our discussion.

Keywords


Adaptive control; chaos stabilization; synchronization; Lyapunov stability theory; hyperchaotic system

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References


H. K. Khalil, Nonlinear Systems. 3rd ed. Prentice Hall, Englewood Cliffs, NJ (2002).

Lorenz, E., Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141 (1963).

Crossref

Andrievskii, B. R., Fradkov, A. l., Control of Chaos: Methods and Applications. Automation and Remote Control, 65(4), 505-533 (2004). Crossref

Aghababa, M. P., Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity, doi: 10.1002/cplx.21533 (2014). Crossref

Vaidyanathan, S., Rajagopal, K., Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control. An International Journal of Optimization and Control: Theories & Applications, 2(1), 17-28 (2012).

Ahmad, I., Saaban, A., Ibrahim, A., Shahzad, M., Global Chaos Synchronization of New Chaotic System using Linear Active Control. Complexity, doi: 10.1002/cplx.21573 (2014). Crossref

Aghababa, M. P., Aghababa, H. P., Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties. Nonlinear Dynamics 67, 2689-2701 (2012). Crossref

Jia, N., Wang, T., Generation and Modified projective Synchronization for a class of New Hyperchaotic Systems. Abstract and Applied Analysis, Article ID 804964, 11 pages (2013).

Shi, X., Wang, Z., Hybrid synchronization phenomenon in two coupled delay hyperchaotic Lorenz systems with unknown parameters via a single linear controller. Journal of Vibrational and Control, 19(7), 1051-1060 (2013). Crossref

Pai, N. S., Yau, H. T., Hybrid synchronization phenomenon in two coupled delay hyperchaotic Lorenz systems with unknown parameters via a single linear controller. Journal of Vibrational and Control, 17(1) 11-17 (2010). Crossref

Al-Hadhrami, S., Saaban, A., Ibrahim, A., Shazad, M., Ahmad, I., Linear Active Control Algorithm to Synchronize a Nonlinear HIV/AIDS Dynamical System. Asian Journal of Applied Sciences and Engineering, 3(2), 96-115 (2014).

Ojo, K. S., Njah, A. N., Ogunjo, O., Comparison of backsteeping and modified active control in projective synchronization of chaos in an extended Bonhoffer-van der Pol Oscillator. Pranam Journal of Physics, 80(5), 825-835 (2013). Crossref

Njah, A. N., Synchronization and Ant-synchronization of double hump Duffing-Van der Pol Oscillator via Active Control. Journal of Information and Computer Science, 4(4), 243-250 (2009).

Idowu, B. A., Vincent, U. E., Synchronization and stabilization of Chaotic Dynamics in Quasi-1D Bose-einstein Condensate. Journal of Chaos, (2013).

Khan, A., Shahzad, M., Synchronization of circular restricted three body problem with Lorenz hyper chaotic system using a robust adaptive sliding mode controller. Complexity, 18, 58-64 (2013). Crossref

Zhao, J., Zhou, D., Li, Y., A new impulsive synchronization of Chen hyper-chaotic system and Lü hyper-chaotic system. Journal of Vibration and Control, 19(12), 1773-1778 (2013). Crossref

Park, J. H., Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. Journal of Computational and Applied mathematics, 213, 288-293 (2008). Crossref

Ahmad, I., Saaban, A., Ibrahim, A., Shahzad, M., Chaos Control and Synchronization of Chaotic System Based upon Adaptive Control Algorithm, Int. Journal of Advances in Tel. comm. Electronics, Signals & Systems, 3(2), 53-62 (2014).

Ying-ying, M., Yun-gang, L., Barbalat's Lemma and its application in analysis of system stability. Journal of Shandong University of Technology, 37(1), 51-55 (2007).




DOI: http://dx.doi.org/10.11121/ijocta.01.2015.00238

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Copyright (c) 2015 Israr Ahmad, Azizan Bin Saaban, Adyda Binti Ibrahim, Said Al-Hadhrami, Mohammad Shahzad, Sharifa Hilal Al-Mahrouqi

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