Technical Brief

The Control and Synchronization of a Rotational Relativistic Chaotic System With Parameter Uncertainties and External Disturbance

[+] Author and Article Information
Runzi Luo, Yanhui Zeng

Department of Mathematics,
Nanchang University,
Nanchang 330031, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 5, 2014; final manuscript received January 25, 2015; published online June 9, 2015. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 10(6), 064503 (Nov 01, 2015) (6 pages) Paper No: CND-14-1281; doi: 10.1115/1.4029702 History: Received November 05, 2014; Revised January 25, 2015; Online June 09, 2015

This paper investigates the control and synchronization of a rotational relativistic chaotic system with parameter uncertainties and external disturbance. By using the proper coordinate transformation, some novel criteria for control or synchronization are proposed via a single input. Numerical simulations are given to show the robustness and efficiency of the proposed approach.

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Yang, T., and Chua, L. O., 1997, “Impulsive Stabilization for Control and Synchronization of Chaotic Systems: Theory and Application to Secure Communication,” IEEE Trans. Circuits Syst., 44(10), pp. 976–988. [CrossRef]
Blasius, B., Huppert, A., and Stone, L., 1999, “Complex Dynamics and Phase Synchronization in Spatially Extended Ecological Systems,” Nature, 399, pp. 354–359. [CrossRef] [PubMed]
Liu, X. W., Huang, Q. Z., Gao, X., and Shao, S. Q., 2007, “Impulsive Control of Chaotic Systems With Exogenous Perturbations,” Chin. Phys., 16(8), pp. 2272–2277. [CrossRef]
Li, C. L., Su, K. L., and Wu, L., 2013, “Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System,” ASME J. Comput. Nonlinear Dyn., 8(3), p. 031005. [CrossRef]
Pan, L., Zhou, L., and Li, D. Q., 2013, “Synchronization of Three-Scroll Unified Chaotic System (TSUCS) and Its Hyper-Chaotic System Using Active Pinning Control,” Nonlinear Dyn., 73(3), pp. 2059–2071. [CrossRef]
Farivar, F., Nekoui, M. A., Shoorehdeli, M. A., and Teshnehlab, M., 2012, “Modified Projective Synchronization of Chaotic Dissipative Gyroscope Systems Via Backstepping Control,” Indian J. Phys., 86(10), pp. 901–906. [CrossRef]
Aghababa, M. P., and Aghababa, H. P., 2013, “Adaptive Finite-Time Synchronization of Non-Autonomous Chaotic Systems With Uncertainty,” ASME J. Comput. Nonlinear Dyn., 8(3), p. 031006. [CrossRef]
Wu, Z. G., and Shi, P., 2013, “Sampled-Data Synchronization of Chaotic Lur'e Systems With Time Delays,” IEEE Trans. Neural Networks Learn. Syst., 24(3), pp. 410–421. [CrossRef]
Chen, S. H., Wang, F., and Wang, C. P., 2004, “Synchronizing Strict-Feedback and General Strict-Feedback Chaotic Systems Via a Single Controller,” Chaos, Solitons Fractals, 20(2), pp. 235–243. [CrossRef]
Wang, G. M., 2010, “Stabilization and Synchronization of Genesio–Tesi System Via Single Variable Feedback Controller,” Phys. Lett. A, 374(28), pp. 2831–2834. [CrossRef]
Lu, J. Q., Ho, D. W. C., Cao, J. D., and Kurths, J., 2013, “Single Impulsive Controller for Globally Exponential Synchronization of Dynamical Networks,” Nonlinear Anal.: Real World Appl., 14(1), pp. 581–593. [CrossRef]
Carmeli, M., 1985, “Field Theory on R×S3Topology. I: The Klein–Gordon and Schrödinger Equations,” Found. Phys., 15(2), pp. 175–184. [CrossRef]
Li, H. B., Wang, B. H., Zhang, Z. Q., Liu, S., and Li, Y. S., 2012, “Combination Resonance Bifurcations and Chaos of Some Nonlinear Relative Rotation System,” Acta Phys. Sin, 61(9), p. 094501 (in Chinese). [CrossRef]
Meng, Z., Fu, L. Y., and Song, M. H., 2013, “Bifurcation of a Kind of Nonlinear-Relative Rotational System With Combined Harmonic Excitation,” Acta Phys. Sin, 62, p. 054501 (in Chinese). [CrossRef]
Liu, S., Zhao, S. S., Sun, B. P., and Zhang, W. M., 2014, “Bifurcation and Chaos Analysis of a Nonlinear Electromechanical Coupling Relative Rotation System,” Chin. Phys., 23(9), p. 094501. [CrossRef]
Luo, R. Z., and He, L. M., 2014, “The Control and Modified Projective Synchronization of a Class of 2,3,4-Dimensional (Chaotic) Systems With Parameter and Model Uncertainties and External Disturbances Via Adaptive Control,” Chin. J. Phys., 52, pp. 830–851. [CrossRef]


Grahic Jump Location
Fig. 1

The chaotic attractor of system (1). (a) Chaotic attractor in (x1; x2; x4) space and (b) chaotic attractor in (x4; x3; x2) space.

Grahic Jump Location
Fig. 2

The phase diagram of system (3). (a) The phase diagram in (x1; x2; x4) space and (b) the phase diagram in (x2; x3; x4) space.

Grahic Jump Location
Fig. 3

The time response of states x1, x2, x3, x4 of system (3)

Grahic Jump Location
Fig. 4

The time evolution of estimated values p∧1,q∧1

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Fig. 5

The time response of controller u

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Fig. 6

The synchronization errors between systems (2) and (13)

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Fig. 7

The time evolution of estimated values p∧1,q∧1

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Fig. 8

The time evolution of estimated values p∧2,q∧2



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