Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller

Applied Mathematics and Computation

Volumn 217, Issue 1, 2010, Pages 164-174

  Zhang, Dong ^a   Xu, Jian ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Chaos; Delay dependent; L K function; Projective synchronization; Sliding mode control

Indexed keywords

CONVERGENCE VELOCITY; DELAY-DEPENDENT; ERROR SYSTEMS; FUNCTIONAL METHODS; GAIN MATRICES; GLOBAL ASYMPTOTIC STABILITY; INTEGRAL SLIDING MODE; INTEGRAL SLIDING MODE CONTROL; K-FUNCTION; L-K FUNCTION; LINEAR MATRIX INEQUALITY TECHNIQUES; LMI TECHNIQUES; LYAPUNOV-KRASOVSKII; PROJECTIVE SYNCHRONIZATION; REACHABILITY; SIMULATION EXAMPLE; SLIDING MODE CONTROLLER; SLIDING MODE SURFACE; SLIDING SURFACE; SUFFICIENT CONDITIONS; SWITCHING SURFACES; TIME-DELAYED NEURAL NETWORKS;

ASYMPTOTIC STABILITY; CONTROLLERS; DELAY CONTROL SYSTEMS; DYNAMICAL SYSTEMS; FREQUENCY SELECTIVE FADING; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; ROBUSTNESS (CONTROL SYSTEMS); SLIDING MODE CONTROL; SYNCHRONIZATION; UNCERTAIN SYSTEMS;

NEURAL NETWORKS;

EID: 77955432342     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.05.037     Document Type: Article

References (46)

1. L.M. Pecora, and T.L. Carroll Synchronization in chaotic systems Phys. Rev. Lett. 64 1990 821 824
2. G.R. Chen, and X. Dong From Chaos to Order: Methodologies, Perspectives, and Applications 1998 World Scientific Singapore
3. T. Yang, and L.O. Chua Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication IEEE Trans. Circuits Syst. I 44 1997 976 988 (Pubitemid 127768200)
4. J.G. Ojalvo, and R. Roy Spatiotemporal communication with synchronized optical chaos Phys. Rev. Lett. 86 2001 5204 5207 (Pubitemid 32527774)
5. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, and C.S. Zhou The synchronization of chaotic systems Phys. Rep. 366 2002 1 101
6. J.C. Sprott Chaos and Time-Series Analysis 2003 Oxford University Press Oxford
7. E. Ott, C. Grebogi, and J.A. Yoke Controlling chaos Phys. Rev. Lett. 64 1990 1196 1199
8. H.G. Schuster Handbook of Chaos Control 1999 Wiley-VCH Weinheim
9. P. Balasubramaniam, and R. Rakkiyappan Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays Appl. Math. Comput. 204 2008 680 686
10. L.Q. Zhou, and G.D. Hu Global exponential periodicity and stability of cellular neural networks with variable and distributed delays Appl. Math. Comput. 195 2008 402 411
11. H. Huang, and J.D. Cao On global asymptotic stability of recurrent neural networks with time-varying delays Appl. Math. Comput. 142 2003 143 154
12. Z. Chen, D.H. Zhao, and X.L. Fu Discrete analogue of high-order periodic Cohen-Grossberg neural networks with delay Appl. Math. Comput. 214 2009 210 217
13. H.T. Lu Chaotic attractors in delayed neural networks Phys. Lett. A 298 2002 109 116
14. M. Gilli Strange attractors in delayed cellular neural networks IEEE Trans. Circuits Syst. I 40 1993 849 853
15. P. Yu, Y. Yuan, and J. Xu Study of double Hopf bifurcation and chaos for an oscillator with time-delayed feedback Commun. Nonlinear Sci. Numer. Simul. 7 2002 69 91
16. H. Huang, and G. Feng Synchronization of nonidentical chaotic neural networks with time delays Neural Networks 22 2009 869 874
17. C.Y. Chee, and D.L. Xu Control of the formation of projective synchronization in lower-dimensional discrete-time systems Phys. Lett. A 318 2003 112 118
18. Q. Wang, and Y. Chen Generalized Q-S (lag, anticipated and complete) synchronization in modified Chua's circuit and Hindmarsh-Rose systems Appl. Math. Comput. 181 2006 48 56
19. D.X. Wang, Y.L. Zhong, and S.H. Chen Lag synchronizing chaotic system based on a single controller Commun. Nonlinear Sci. Numer. Simul. 13 2008 637 644
20. D. Ghosh, A.R. Chowdhury, and P. Saha On the various kinds of synchronization in delayed Duffing-Van der Pol system Commun. Nonlinear Sci. Numer. Simul. 13 2008 790 803
21. M.M.A. Sawalha, and M.S.M. Noorani Anti-synchronization of two hyperchaotic systems via nonlinear control Commun. Nonlinear Sci. Numer. Simul. 14 2009 3402 3411
22. X. Huang, and J.D. Cao Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme Nonlinearity 19 2006 2797 2811
23. D. Ghosh Generalized projective synchronization in time-delayed systems: nonlinear observer approach Chaos 19 2009 013102
24. J.M. Gonzalez-Miranda Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving Phys. Rev. E 57 1998 7321 7324
25. R. Mainieri, and J. Rehacek Projective synchronization in three-dimensional chaotic systems Phys. Rev. Lett. 82 1999 3042 3045
26. J.P. Yan, and C.P. Li Generalized projective synchronization of a unified chaotic system Chaos Solitons Fract. 26 2005 1119 1124
27. G.H. Li Generalized projective synchronization of two chaotic systems by using active control Chaos Solitons Fract. 30 2006 77 82
28. V.V. Astakhov, V.S. Anishchenko, T. Kapitaniak, and A.V. Shabunin Synchronization of chaotic oscillators by periodic parametric perturbations Phys. D 109 1997 11 16
29. X.S. Yang, C.K. Duan, and X.X. Liao A note on mathematical aspects of drive-response type synchronization Chaos Solitons Fract. 10 1999 1457 1462
30. H.G. Zhang, Y.H. Xie, Z.L. Wang, and C.D. Zheng Adaptive synchronization between two different chaotic neural networks with time delay IEEE Trans. Neural Networks 18 2007 1841 1845
31. X.R. Han, E. Fridman, S.K. Spurgeon, and C. Edwards On the design of sliding mode static-output-feedback controllers for systems with state-delay IEEE Trans. Ind. Electron. 56 2009 3656 3664
32. M. Roopaei, M.Z. Jahromi, R. John, and T.C. Lin Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input Commun. Nonlinear Sci. Numer. Simul. 15 2010 2536 2545
33. N. Cai, Y.W. Jing, and S.Y. Zhang Modified projective synchronization of chaotic systems with disturbances via active sliding mode control Commun. Nonlinear Sci. Numer. Simul. 15 2010 1613 1620
34. G.H. Li, S.P. Zhou, and K. Yang Generalized projective synchronization between two different chaotic systems using active backstepping control Phys. Lett. A 355 2006 326 330
35. M. Roopaei, and M.Z. Jahromi Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control Chaos 18 2008 033133
36. Y.Q. Yang, and J.D. Cao Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects Phys. A 386 2007 492 502
37. V.I. Utkin Variable structure systems with sliding modes IEEE Trans. Autom. Control 22 1977 212 222
38. J. Meng, and X.Y. Wang Generalized projective synchronization of a class of delayed neural networks Mod. Phys. Lett. B 22 2008 181 190
39. C.F. Feng, Y. Zhang, J.T. Sun, W. Qi, and Y.H. Wang Generalized projective synchronization in time-delayed chaotic systems Chaos Solitons Fract. 38 2008 743 747
40. S.Q. Zhu, C.H. Zhang, Z.L. Cheng, and J. Feng Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems IEEE Trans. Autom. Control 52 2007 880 885
41. E. Fridman Effects of small delays on stability of singularly perturbed systems Automatica 38 2002 897 902
42. E. Fridman, and U. Shaked H-infinity control of linear state-delay descriptor systems: an LMI approach Linear Algebra Appl. 351-352 2002 271 302
43. E. Fridman Stability of linear descriptor systems with delay: A Lyapunov-based approach J. Math. Anal. Appl. 273 2002 24 44
44. V.I. Utkin Sliding Modes in Control and Optimization 1992 Springer-Verlag New York
45. J. Hale, and S. Lunel Introduction to the Theory of Functional Differential Equations 1991 Springer-Verlag New York
46. N. Olgac, and V.R. Iragavarapu Sliding mode control with backlash and saturation laws Int. J. Robot Autom. 10 1995 49 55