Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 40, Issue 3, 2010, Pages 831-844

  Zhang, Huaguang ^a   Ma, Tiedong ^a   Huang, Guang Bin ^b   Wang, Zhiliang ^a  

^a NORTHEASTERN UNIVERSITY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Chaos synchronization; Chaotic delayed neural networks (DNNs); Dual stage impulsive control; Impulsive functional differential equations (FDEs); Linear matrix inequality (LMI); Parametric uncertainty

Indexed keywords

CHAOS SYNCHRONIZATION; DELAYED NEURAL NETWORKS; DUAL STAGE; IMPULSIVE CONTROLS; IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATION; PARAMETRIC UNCERTAINTIES;

ALGORITHMS; CHAOTIC SYSTEMS; DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; ROBUSTNESS (CONTROL SYSTEMS); SYNCHRONIZATION; UNCERTAIN SYSTEMS;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; FEEDBACK SYSTEM; NONLINEAR SYSTEM; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS;

EID: 77952582245     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2009.2030506     Document Type: Article

References (58)

1. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, "The synchronization of chaotic systems, " Phys. Rep., vol. 366, no. 1/2, pp. 1-101, Aug. 2002.
2. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications. Singapore: World Scientific, 1998.
3. E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos, " Phys. Rev. Lett., vol. 64, no. 11, pp. 1196-1199, Mar. 1990.
4. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems, " Phys. Rev. Lett., vol. 64, no. 8, pp. 821-824, Feb. 1990.
5. T. Huang, C. Li, and X. Liu, "Synchronization of chaotic systems with delay using intermittent linear state feedback, " Chaos, vol. 18, no. 3, p. 033122, Sep. 2008.
6. C. Cheng, T. Liao, J. Yan, and C. C. Hwang, "Exponential synchronization of a class of neural networks with time-varying delays, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 36, no. 1, pp. 209-215, Feb. 2006. (Pubitemid 43174154)
7. J. Liang, Z. Wang, Y. Liu, and X. Liu, "Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 4, pp. 1073-1083, Aug. 2008.
8. J. Meng and X. Wang, "Generalized synchronization via nonlinear control, " Chaos, vol. 18, no. 2, p. 023 108, Jun. 2008.
9. U. E. Vincent, A. Ucar, J. A. Laoye, and S. O. Kareem, "Control and synchronization of chaos in RCL-shunted Josephson junction using backstepping design, " Phys. C, vol. 468, no. 5, pp. 374-382, Mar. 2008.
10. M. T. Yassen, "Controlling, synchronization and tracking chaotic Liu system using active backstepping design, " Phys. Lett. A, vol. 360, no. 4/5, pp. 582-587, Jan. 2007.
11. M. S. Tavazoei and M. Haeri, "Synchronization of chaotic fractionalorder systems via active sliding mode controller, " Phys. A, vol. 387, no. 1, pp. 57-70, Jan. 2008.
12. M. Roopaei and M. Zolghadri Jahromi, "Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control, " Chaos, vol. 18, no. 3, p. 033133, Sep. 2008.
13. H. Zhang, W. Huang, Z. Wang, and T. Chai, "Adaptive synchronization between two different chaotic systems with unknown parameters, " Phys. Lett. A, vol. 350, no. 5/6, pp. 363-366, Feb. 2006. (Pubitemid 43129366)
14. H. Zhang, Y. Xie, Z. Wang, and C. Zheng, "Adaptive synchronization between two different chaotic neural networks with time delay, " IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1841-1845, Nov. 2007. (Pubitemid 350148432)
15. J. Lu, J. Cao, and D. Ho, "Adaptive stabilization and synchronization for chaotic Lur'e systems with time-varying delay, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 5, pp. 1347-1356, Jun. 2008.
16. X. Liang, J. Zhang, and X. Xia, "Adaptive synchronization for generalized Lorenz systems, " IEEE Trans. Autom. Control, vol. 53, no. 7, pp. 1740-1746, Aug. 2008.
17. J. Zhou, J. Lu, and J. Lü, "Pinning adaptive synchronization of a general complex dynamical network, " Automatica, vol. 44, no. 4, pp. 996-1003, Apr. 2008.
18. J. Zhou, J. Lu, and J. Lü, "Adaptive synchronization of an uncertain complex dynamical network, " IEEE Trans. Autom. Control, vol. 51, no. 4, pp. 652-656, Apr. 2006.
19. J. Cao and J. Lu, "Adaptive synchronization of neural networks with or without time-varying delay, " Chaos, vol. 16, no. 1, p. 013133, Mar. 2006.
20. H. Zhang, T. Ma, W. Yu, and J. Fu, "A practical approach to robust impulsive lag synchronization between different chaotic systems, " Chin. Phys. B, vol. 17, no. 10, pp. 3616-3622, Oct. 2008.
21. M. Haeri and M. Dehghani, "Impulsive synchronization of different hyperchaotic (chaotic) systems, " Chaos Solitons Fractals, vol. 38, no. 1, pp. 120-131, Oct. 2008. (Pubitemid 351503973)
22. J. G. Lu and D. J. Hill, "Impulsive synchronization of chaotic Lur'e systems by linear static measurement feedback: An LMI approach, " IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 8, pp. 710-714, Aug. 2007.
23. T. Ma, H. Zhang, and Z. Wang, "Impulsive synchronization for unified chaotic systems with channel time-delay and parameter uncertainty, " Acta Phys. Sin., vol. 56, no. 7, pp. 3796-3802, Jul. 2007.
24. B. Liu, X. Liu, G. Chen, and H. Wang, "Robust impulsive synchronization of uncertain dynamical networks, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 7, pp. 1431-1441, Jul. 2005. (Pubitemid 41081627)
25. C. Li, X. Liao, and X. Yang, "Impulsive stabilization and synchronization of a class of chaotic delay systems, " Chaos, vol. 15, no. 4, p. 043103, Dec. 2005.
26. C. Li, L. Chen, and K. Aihara, "Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks, " Chaos, vol. 18, no. 2, p. 023132, Jun. 2008.
27. U. E. Vincent, "Synchronization of identical and non-identical 4-D chaotic systems using active control, " Chaos Solitons Fractals, vol. 37, no. 4, pp. 1065-1075, Aug. 2008.
28. A. N. Njah and U. E. Vincent, "Chaos synchronization between single and double wells Duffing-Van der Pol oscillators using active control, " Chaos Solitons Fractals, vol. 37, no. 5, pp. 1356-1361, Sep. 2008.
29. W. Perruquetti, T. Floquet, and E. Moulay, "Finite-time observers: Application to secure communication, " IEEE Trans. Autom. Control, vol. 53, no. 1, pp. 356-360, Feb. 2008.
30. A. L. Fradkov, B. Andrievsky, and R. J. Evans, "Adaptive observer-based synchronization of chaotic systems with first-order coder in the presence of information constraints, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 6, pp. 1685-1694, Jul. 2008.
31. X. Wang and J. Meng, "Observer-based adaptive fuzzy synchronization for hyperchaotic systems, " Chaos, vol. 18, no. 3, p. 033102, Sep. 2008.
32. J. Meng and X. Wang, "Generalized projective synchronization of chaotic neural networks: Observer-based approach, " Mod. Phys. Lett. B, vol. 22, no. 3, pp. 181-190, 2008.
33. Z. Yang and D. Xu, "Stability analysis and design of impulsive control systems with time delays, " IEEE Trans. Autom. Control, vol. 52, no. 8, pp. 1448-1454, Aug. 2007. (Pubitemid 47316692)
34. M. Gilli, "Strange attractors in delayed cellular neural networks, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 11, pp. 849-853, Nov. 1993.
35. H. Lu, "Chaotic attractors in delayed neural networks, " Phys. Lett. A, vol. 298, no. 2/3, pp. 109-116, Jun. 2002.
36. F. Zou and J. A. Nossek, "Bifurcation and chaos in cellular neural networks, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 40, no. 3, pp. 166-173, Mar. 1993.
37. Y. Shen and J. Wang, "Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters, " IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1857-1862, Nov. 2007.
38. Y. Shen and J. Wang, "An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays, " IEEE Trans. Neural Netw., vol. 19, no. 3, pp. 528-531, Mar. 2008. (Pubitemid 351411576)
39. C. Li, G. Feng, and T. Huang, "On hybrid impulsive and switching neural networks, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 6, pp. 1549-1560, Dec. 2008.
40. W. Yu, J. Cao, and J. Lü, "Global synchronization of linearly hybrid coupled networks with time-varying delay, " SIAM J. Appl. Dyn. Syst., vol. 7, no. 1, pp. 108-133, Jan. 2008.
41. J. Cao, G. Chen, and P. Li, "Global synchronization in an array of delayed neural networks with hybrid coupling, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 2, pp. 488-498, Apr. 2008. (Pubitemid 351479567)
42. Y. Liu, Z. Wang, J. Liang, and X. Liu, "Synchronization and state estimation for discrete-time complex networks with distributed delays, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 5, pp. 1314-1325, Oct. 2008.
43. Y. Sun, J. Cao, and Z. Wang, "Exponential synchronization of stochastic perturbed chaotic delayed neural networks, " Neurocomputing, vol. 70, no. 13-15, pp. 2477-2485, Aug. 2007. (Pubitemid 46825362)
44. J. Lu and J. Cao, "Synchronization-based approach for parameters identification in delayed chaotic neural networks, " Phys. A, vol. 382, no. 2, pp. 672-682, Aug. 2007. (Pubitemid 46936089)
45. Y. Tang, R. Qiu, J. Fang, Q. Miao, and M. Xia, "Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays, " Phys. Lett. A, vol. 372, no. 24, pp. 4425-4433, Jun. 2008.
46. J. Lü and G. Chen, "A time-varying complex dynamical network model and its controlled synchronization criteria, " IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 841-846, Jun. 2005.
47. H. Huang, H. Li, and J. Zhong, "Master-slave synchronization of general Lur'e systems with time-varying delay and parameter uncertainty, " Int. J. Bifurc. Chaos, vol. 16, no. 2, pp. 281-294, Feb. 2006.
48. T. Ma, H. Zhang, and J. Fu, "Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty, " Chin. Phys. B, vol. 17, no. 12, pp. 4407-4417, Dec. 2008.
49. Y. Li, X. Liao, C. Li, T. Huang, and D. Yang, "Impulsive synchronization and parameter mismatch of the three-variable autocatalator model, " Phys. Lett. A, vol. 366, no. 1/2, pp. 52-60, Jun. 2007.
50. X. Wu and M. Wang, "Robust synchronization of chaotic Lur'e systems via replacing variables control, " Int. J. Bifurc. Chaos, vol. 16, no. 11, pp. 3421-3433, Nov. 2006.
51. J. A. K. Suykens, P. F. Curran, and L. O. Chua, "Robust synthesis for master-slave synchronization of Lur'e systems, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 46, no. 7, pp. 841-850, Jul. 1999.
52. X. Wu, J. Cai, and M. Wang, "Robust synchronization of chaotic horizontal platform systems with phase difference, " J. Sound Vib., vol. 305, no. 3, pp. 481-491, Aug. 2007. (Pubitemid 47071919)
53. E. N. Sanchez and J. P. Perez, "Input-to-state stability (ISS) analysis for dynamics NN, " IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 46, no. 11, pp. 1395-1398, Nov. 1999.
54. X. Guan and C. Chen, "Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, " IEEE Trans. Fuzzy Syst., vol. 12, no. 2, pp. 236-249, Apr. 2004.
55. J. Lam, H. Gao, and C. Wang, "Stability analysis for continuous systems with two additive time-varying delay components, " Syst. Control Lett., vol. 56, no. 1, pp. 16-24, Jan. 2007.
56. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
57. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations. Singapore: World Scientific, 1989.
58. H. K. Khalil, Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002.