0
Research Papers

The Control and Synchronization of a Class of Chaotic Systems With Output Variable 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 September 5, 2015; final manuscript received December 31, 2015; published online February 3, 2016. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 11(5), 051011 (Feb 03, 2016) (7 pages) Paper No: CND-15-1274; doi: 10.1115/1.4032444 History: Received September 05, 2015; Revised December 31, 2015

This paper investigates the control and synchronization of a class of chaotic systems with external disturbance. The chaotic systems are assumed that only the output state variable is available. By using the output state variable, two types synchronization schemes, i.e., the chaos-based synchronization and the observer-based synchronization schemes, are discussed. Some novel criteria for the control and synchronization of a class of chaotic systems with external disturbance are proposed. The unified chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Pecora, L. M. , and Carroll, T. L. , 1990, “ Synchronization in Chaotic Systems,” Phys. Rev. Lett., 64, pp. 821–824. [CrossRef] [PubMed]
Ott, E. , Grebogi, C. , and Yorke, J. A. , 1990, “ Controlling Chaos,” Phys. Rev. Lett., 64(11), pp. 1196–1199. [CrossRef] [PubMed]
Rafikov, M. , and Balthazar, J. M. , 2008, “ On Control and Synchronization in Chaotic and Hyperchaotic Systems Via Linear Feedback Control,” Commun. Nonlinear Sci. Numer. Simul., 13(7), pp. 1246–1255. [CrossRef]
Wen, C. , Zhou, J. , Liu, Z. , and Su, H. , 2011, “ Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance,” IEEE Trans. Autom. Control, 56(7), pp. 1672–1678. [CrossRef]
Srivastava, M. , Ansari, S. P. , Agrawal, S. K. , Das, S. , and Leung, A. Y. T. , 2014, “ Anti-Synchronization Between Identical and Non-Identical Fractional-Order Chaotic Systems Using Active Control Method,” Nonlinear Dyn., 76(2), pp. 905–914. [CrossRef]
Rafikov, M. , and Balthazar, J. M. , 2004, “ On an Optimal Control Design for Röossler System,” Phys. Lett. A, 333, pp. 241–245. [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]
Grzybowski, J. M. V. , Rafikov, M. , and Balthazar, J. M. , 2009, “ Synchronization of the Unified Chaotic System and Application in Secure Communication,” Commun. Nonlinear Sci. Numer. Simul., 14(6), pp. 2793–2806. [CrossRef]
Vincent, U. E. , 2008, “ Synchronization of Identical and Nonidentical 4-D Chaotic Systems Using Active Control,” Chaos Solitons Fractals, 37(4), pp. 1065–1075. [CrossRef]
Luo, R. Z. , and Zeng, Y. H. , 2015, “ The Control and Synchronization of a Rotational Relativistic Chaotic System With Parameter Uncertainties and External Disturbance,” ASME J. Comput. Nonlinear Dyn., 10(6), p. 064503. [CrossRef]
Song, Q. K. , and Huang, T. W. , 2015, “ Stabilization and Synchronization of Chaotic Systems With Mixed Time-Varying Delays Via Intermittent Control With Non-Fixed Both Control Period and Control Width,” Neurocomputing, 154, pp. 61–69. [CrossRef]
Sadaoui, D. , Boukabou, A. , and Hadef, S. , 2014, “ Predictive Feedback Control and Synchronization of Hyperchaotic Systems,” Appl. Math. Comput., 247, pp. 235–243. [CrossRef]
Luo, R. Z. , and Zhang, C. H. , 2015, “ The Observer of a Class of Chaotic Systems: An Application to HR Neuronal Model,” Chin. Phys. B, 24(3), p. 030503. [CrossRef]
Luo, R. Z. , and Zeng, Y. H. , 2015, “ The Control and Synchronization of a Rotational Relativistic Chaotic System Via States Recovery,” Chin. J. Phys., 53, p. 040704.
Luo, R. Z. , and Zeng, Y. H. , 2015, “ The Control and Synchronization of a Class of Chaotic System Via States Recovery,” Chin. J. Phys., 53, p. 060704.
Luo, R. Z. , and He, L. M. , 2014, “ PC Synchronization of a Class of Chaotic Systems Via Event-Triggered Control,” Chin. Phys. B, 23(7), p. 070506. [CrossRef]
Lorenz, E. N. , 1963, “ Deterministic Nonperiodic Flow,” J. Atmos. Sci., 20(2), pp. 130–141. [CrossRef]
Chen, G. , and Ueta, T. , 1999, “ Yet Another Chaotic Attractor,” Int. J. Bifurcation Chaos, 9(07), pp. 1465–1466. [CrossRef]
Lü, J. H. , Chen, G. R. , Cheng, D. Z. , and Celikovsky, S. , 2002, “ Bridge the Gap Between the Lorenz System and the Chen System,” Int. J. Bifurcation Chaos, 12(12), pp. 2917–2926. [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.
Park, K. B. , and Tsuji, T. , 1999, “ Terminal Sliding Mode Control of Second-Order Nonlinear Uncertain Systems,” Int. J. Robust Nonlinear Control, 9(11), pp. 769–780. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Orbits of controlled system (26) with x1(0)=1,x2(0)=2,x3(0)=3,ρ(0)=0

Grahic Jump Location
Fig. 2

Plots of synchronization errors between systems (27) and (28)

Grahic Jump Location
Fig. 3

Plots of synchronization errors between systems (27) and (29)

Grahic Jump Location
Fig. 4

Plots of synchronization errors between systems (27) and (30)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In