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Finite-Time Chaos Control for a Chaotic Complex-Variable System

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Abstract

In this paper, we investigate the finite-time stabilization of complex-variable Lorenz system, which is a chaotic system and exhibits chaotic attractors. Based on the finite-time stability theory, an adaptive control technique is presented to achieve finite-time stabilization for chaotic complex-variable system. The significant contribution of this paper is using the ultimate bound set in finite-time chaos control. In fact, we apply the estimated bound set, to the finite-time stabilization of the complex Lorenz system. Simulation results show the effectiveness of the proposed method.

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References

  • Aghababa, M. P., & Aghababa, H. P. (2012). Finite-time stabilization of a non-autonomous chaotic rotating mechanical system. Journal of the Franklin Institute, 349, 2875–2888.

    Article  MathSciNet  MATH  Google Scholar 

  • Balthazar, J. M., Tusset, A. M., & Bueno, A. M. (2014). TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination. Journal of Theoretical and Applied Mechanics, 52(1), 93–106.

    Google Scholar 

  • Bhat, S. P., & Bernstein, D. S. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 38(3), 751–766.

    Article  MathSciNet  MATH  Google Scholar 

  • Chuang, C. F., Sun, Y. J., & Wang, W. J. (2012). A novel synchronization scheme with a simple linear control and guaranteed convergence time for generalized Lorenz chaotic systems. Chaos, 22, 043108.

    Article  Google Scholar 

  • Effati, S., Saberi-Nadjafi, J., & Saberi Nik, H. (2014). Optimal and adaptive control for a kind of 3D chaotic and 4D hyper-chaotic systems. Applied Mathematical Modelling, 38, 759–774.

    Article  MathSciNet  Google Scholar 

  • Feng, Y., Yu, X., & Man, Z. (2002). Non-singular terminal sliding mode control of rigid manipulators. Automatica, 38(12), 2159–2167.

    Article  MathSciNet  MATH  Google Scholar 

  • Fowler, A. C., Gibbon, J. D., & McGuinness, M. J. (1982). The complex Lorenz equations. Physica D, 4(2), 139–163.

    Article  MathSciNet  MATH  Google Scholar 

  • Hong, Y., & Jiang, Z. (2006). Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties. IEEE Transactions on Automatic Control, 51(12), 1950–1956.

    Article  MathSciNet  Google Scholar 

  • Huang, X., Lin, W., & Yang, B. (2005). Global finite-time stabilization of a class of uncertain nonlinear systems. Automatica, 41(5), 881–888.

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, C. F., Cheng, K. H., & Yan, J. J. (2009). Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties. Communications in Nonlinear Science and Numerical Simulation, 14(6), 2784–2792.

    Article  Google Scholar 

  • Lee, S. H., Park, J. B., & Choi, Y. H. (2009). Finite time control of nonlinear underactuated systems using terminal sliding surface. In IEEE international symposium on industrial electronics (pp. 626–631). Seoul Olympic Parktel, Seoul.

  • Li, R. H., Chen, W. S., & Li, S. (2013). Finite-time stabilization for hyper-chaotic Lorenz system families via adaptive control. Applied Mathematical Modelling, 37, 1966–1972.

    Article  MathSciNet  Google Scholar 

  • Mahmoud, G. M., Bountis, T., & Mahmoud, E. E. (2007). Active control and global synchronization for complex Chen and Lü systems. International Journal of Bifurcation and Chaos, 17, 4295–4308.

    Article  MathSciNet  Google Scholar 

  • Mahmoud, G. M., & Mahmoud, E. E. (2007). Basic properties and chaotic synchronization of complex Lorenz system. International Journal of Modern Physics, 18(2), 253–265.

    Article  MathSciNet  MATH  Google Scholar 

  • Mahmoud, G. M., Mahmoud, E. E., & Ahmed, M. E. (2009). On the hyperchaotic complex Lü system. Nonlinear Dynamics, 58, 725–738.

    Article  MathSciNet  MATH  Google Scholar 

  • Ning, C. Z., & Haken, H. (1990). Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. Physical Review A, 41, 3826–3837.

    Article  Google Scholar 

  • Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64, 1196–1199.

    Article  MathSciNet  MATH  Google Scholar 

  • Rafikov, M., & Balthazar, J. M. (2008). On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Communications in Nonlinear Science and Numerical Simulation, 13(7), 1246–1255.

    Article  MathSciNet  MATH  Google Scholar 

  • Roopaei, M., Sahraei, B. R., & Lin, T. C. (2010). Adaptive sliding mode control in a novel class of chaotic systems. Communications in Nonlinear Science and Numerical Simulation, 15, 4158–4170.

    Article  MathSciNet  MATH  Google Scholar 

  • Saberi Nik, H., Effati, S., & Saberi-Nadjafi, J. (2015a). Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization. Complexity, 20(4), 30–44.

    Article  MathSciNet  Google Scholar 

  • Saberi Nik, H., Effati, S., Saberi-Nadjafi, J. (2015b). Ultimate bound sets and exponential finite-time synchronization for a complex chaotic system. Journal of Complexity. doi:10.1016/j.jco.2015.03.001.

  • Saberi Nik, H., Van Gorder, R.A., & Gambino, G. (2015c). The chaotic Dadras-Momeni system: Control and hyperchaotification. IMA Journal of Mathematical Control and Information. doi:10.1093/imamci/dnu050

  • Wang, H., Han, Z. Z., Xie, Q. Y., & Zhang, W. (2009). Finite-time chaos control via nonsingular terminal sliding mode control. Communications in Nonlinear Science and Numerical Simulation, 14(6), 2728–2733.

  • Yassen, M. T. (2007). Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Physics Letters A, 360, 582–587.

    Article  Google Scholar 

  • Yu, W. (2010). Finite-time stabilization of three-dimensional chaotic systems based on CLF. Physics Letters A, 374, 3021–3024.

    Article  MathSciNet  MATH  Google Scholar 

  • Yu, W. G. (2010). Stabilization of three-dimensional chaotic systems via single state feedback controller. Physics Letters A, 374, 1488–1492.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

    Hassan Saberi Nik

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  1. Hassan Saberi Nik
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Correspondence to Hassan Saberi Nik.

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Saberi Nik, H. Finite-Time Chaos Control for a Chaotic Complex-Variable System. J Control Autom Electr Syst 26, 371–379 (2015). https://doi.org/10.1007/s40313-015-0182-6

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  • DOI: https://doi.org/10.1007/s40313-015-0182-6

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