Skip to main content
SpringerLink
Log in
Book cover

Stability and Synchronization Control of Stochastic Neural Networks pp 93–151Cite as

Adaptive Synchronization of Neural Networks

  • Chapter
  • First Online:

  • 1094 Accesses

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 35))

Abstract

The adaptive control strategy has been widely adopted due to its well performance in uncertain systems such as stochastic systems or nonlinear systems. In this chapter, adaptive control is designed for the synchronization of some kinds of neural networks including BAMDNN, SDNN with Markovian switching and T-S fuzzy NN.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. J. Cao, P. Li, W. Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. Lett. A 353(4), 318–325 (2006)

    Article  Google Scholar 

  2. J. Cao, X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Phys. D 212(1), 54–65 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Cao, J. Lu, Adaptive synchronization of neural networks with or without time-varying delays. Chaos: Interdiscip. J. Nonlinear Sci. 16(1), 013133–013139 (2006)

    Article  MathSciNet  Google Scholar 

  4. J. Cao, L. Wang, Periodic oscillatory solution of bidirectional associative memory networks with delays. Phys. Rev. E 61(2), 1825–1828 (2000)

    Article  MathSciNet  Google Scholar 

  5. J. Cao, Z. Wang, Y. Sun, Synchronization in an array of linearly stochastically coupled networks with time-delays. Phys. A: Stat. Mech. Appl. 385(2), 718–728 (2007)

    Article  MathSciNet  Google Scholar 

  6. G. Chen, J. Zhou, Z. Liu, Classification of chaos in 3-d autonomous quadratic systems-I: basic framework and methods. Int. J. Bifurc. Chaos 16(9), 2459–2479 (2006)

    Article  MATH  Google Scholar 

  7. G.R. Chen, J. Zhou, Z.R. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN model. Int. J. Bifurc. Chaos 14(7), 2229–2240 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Chen, D. Zhou, Synchronization in uncertain complex networks. Chaos: Interdiscip. J. Nonlinear Sci. 16(1), 013101 (2006)

    Article  Google Scholar 

  9. T. Chen, L. Wang, Power-rate global stability of dynamical systems with unbounded time-varying delays. IEEE Trans. Circuits Syst. II: Express Briefs 54(8), 705–709 (2007)

    Article  Google Scholar 

  10. M. Gilli, Strange attractors in delayed cellular neural networks. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 40(17), 849–853 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. K. Gopalsamy, Stability of artificial neural networks with impulses. Appl. Math. Comput. 154(3), 783–813 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Gopalsamy, X. He, Delay-independent stability in bidirectional associative memory networks. IEEE Trans. Neural Netw. 5(6), 998–1002 (1994)

    Article  Google Scholar 

  13. H. Huang, D.W.C. Ho, Y. Qu, Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw. 20(7), 799–809 (2007)

    Article  MATH  Google Scholar 

  14. H.R. Karimi, P. Maass, Delay-range-dependent exponential \({H}_\infty \) synchronization of a class of delayed neural networks. Chaos, Solitons Fractals 41(3), 1125–1135 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. J.H. Kim, C.H. Hyun, E. Kim, M. Park, Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15(3), 359–369 (2007)

    Article  Google Scholar 

  16. B. Kosko, Adaptive bi-directional associative memories. Appl. Opt. 26(23), 4947–4960 (1987)

    Article  Google Scholar 

  17. G.H. Li, Modified projective synchronization of chaotic system. Chaos, Solitons Fractals 32(5), 1786–1790 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. P. Li, J. Cao, Z. Wang, Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Phys. A 373, 261–272 (2007)

    Article  Google Scholar 

  19. X. Li, J. Cao, Adaptive synchronization for delayed neural networks with stochastic perturbation. J. Frankl. Inst. 354(7), 779–791 (2008)

    Article  MathSciNet  Google Scholar 

  20. X. Liao, J. Yu, Qualitative analysis of bi-directional associative memory with time delay. Int. J. Circuit Theory Appl. 26(3), 219–229 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. B. Liu, X.Z. Liu, G.R. Chen, Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I 52(7), 1431–1441 (2005)

    Article  MathSciNet  Google Scholar 

  22. Z.G. Liu, Global attractors of delayed BAM neural networks with reaction-diffusion terms. J. Xiangnan Univ. 31(2), 5–11 (2010)

    Google Scholar 

  23. X. Lou, B. Cui, Synchronization of neural networks based on parameter identification and via output or state coupling. J. Comput. Appl. Math. 222(2), 440–457 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. H. Lu, Chaotic attractors in delayed neural networks. Phys. Lett. A 298(2–3), 109–116 (2002)

    Article  MATH  Google Scholar 

  25. J. Lu, D.W.C. Ho, J. Cao, J. Kurths, Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans. Neural Netw. 22(2), 329–336 (2011)

    Article  Google Scholar 

  26. Y. Lu, K. Yi, Adaptive projective synchronization of uncertain Rössler chaotic system. Comput. Sci. 36(5), 91–193 (2009)

    MathSciNet  Google Scholar 

  27. X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Switching (Imperial College Press, London, 2006)

    Book  MATH  Google Scholar 

  28. M.J. Park, O. Kwon, J.H. Park, S.M. Lee, Simplified stability criteria for fuzzy Markovian jumping Hopfield neural networks of neutral type with interval time-varying delays. Expert Syst. Appl. 39(5), 5625–5633 (2012)

    Article  MathSciNet  Google Scholar 

  29. L.M. Pecora, T.L. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  30. K. Sun, S. Qiu, L. Yin, Adaptive function projective synchronization and parameter identification for chaotic systems. Inf. Control 39(3), 326–331 (2010)

    Google Scholar 

  31. Y. Sun, J. Cao, Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation. Phys. Lett. A 364(3), 277–285 (2007)

    Article  MATH  Google Scholar 

  32. Y. Sun, J. Cao, Z. Wang, Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70(13), 2477–2485 (2007)

    Article  Google Scholar 

  33. Y. Sun, G. Feng, J. Cao, Stochastic stability of Markovian switching genetic regulatory networks. Phys. Lett. A 373(18), 1646–1652 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Y. Tang, J. Fang, Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling. Commun. Nonlinear Sci. Numer. Simul. 14(9), 3615–3628 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. F. Wang, H.Y. Wu, Existence and stablity of periodic solution for BAM neural networks. Comput. Eng. Appl. 46(24), 15–18 (2010)

    MATH  Google Scholar 

  36. K. Wang, Z. Teng, H. Jiang, Adaptive synchronization of neural networks with time-varying delay and distributed delay. Phys. A: Stat. Mech. Appl. 387(2–3), 631–642 (2008)

    Article  Google Scholar 

  37. W. Wang, J. Cao, Synchronization in an array of linearly coupled networks with time-varying delay. Phys. A 366, 197–211 (2006)

    Article  Google Scholar 

  38. X.Y. Wang, Q.A. Zhao, Class of uncertain delayed neural network adaptive projection synchronization. Acta Phys. Sin. 57(5) (2008)

    Google Scholar 

  39. Z. Wang, J. Fang, X. Liu, Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos, Solitons Fractals 36(2), 388–396 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  40. Z. Wang, D.W.C. Ho, X. Liu, State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16(1), 279–284 (2005)

    Article  Google Scholar 

  41. Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos, Solitons Fractals 32(1), 62–72 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. Z. Wang, Y. Liu, F. Karl, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354(4), 288–297 (2006)

    Article  MATH  Google Scholar 

  43. Z. Wang, Y. Liu, L. Liu, X. Liu, Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356(4), 346–352 (2006)

    Article  MATH  Google Scholar 

  44. Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4), 299–308 (2005)

    Article  MATH  Google Scholar 

  45. Z. Wang, Y. Liu, X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010)

    Article  Google Scholar 

  46. Z. Wang, Y. Liu, G. Wei, X. Liu, A note on control of discrete-time stochastic systems with distributed delays and nonlinear disturbances. Automatica 46(3), 543–548 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  47. Z. Wang, H. Shu, J. Fang, X. Liu, Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal.: Real World Appl. 7(5), 1119–1128 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  48. Z. Wang, H. Shu, Y. Liu, D.W.C. Ho, X. Liu, Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos, Solitons Fractals 30(4), 886–896 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  49. Z.D. Wang, D.W.C. Ho, Y.R. Liu, X.H. Liu, Robust \({H}_\infty \) control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. Automatica 45(3), 1–8 (2010)

    MathSciNet  Google Scholar 

  50. C.W. Wu, Synchronization in array of coupled nonlinear system with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst. 52(5), 282–286 (2005)

    Article  Google Scholar 

  51. H.J. Xiang, Exponential stablity of fuzzy BAM neural networks with diffusion. J. Xiangnan Univ. 31(2), 12–19 (2010)

    Google Scholar 

  52. D. Xu, Z. Li, Controlled projective synchronization in nonpartially-linear chaotic systems. Int. J. Bifurc. Chaos 12(06), 1395–1402 (2002)

    Article  Google Scholar 

  53. L.X. Yang, W.S. He, X.J. Liu, H.B. Chen, Improved full state hybrid projective synchronization in autonomous chaotic systems. J. Xianyang Norm. Univ. 25(2), 28–30 (2010)

    Google Scholar 

  54. W. Yu, J. Cao, Synchronization control of stochastic delayed neural networks. Phys. A 373, 252–260 (2007)

    Article  Google Scholar 

  55. C. Yuan, X. Mao, Robust stability and controllability of stochastic differential delay equations with Markovian switching. Automatica 40(3), 343–354 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  56. H. Zhang, Y. Wang, D. Liu, Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple time delays. IEEE Trans. Syst., Man Cybern., Part B 38(1), 125–140 (2008)

    Article  MATH  Google Scholar 

  57. J. Zhang, Y. Yang, Global stability analysis of bidirectional associative memory neural networks with time delay. Int. J. Circuit Theory Appl. 29(2), 185–196 (2001)

    Article  MATH  Google Scholar 

  58. L. Zhang, E. Boukas, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45(2), 463–468 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  59. W. Zhang, Y. Tang, J. Fang, Stochastic stability of Markovian jumping genetic regulatory networks with mixed time delays. Appl. Math. Comput. 217(17), 7210–7225 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  60. H. Zhao, S. Xu, Y. Zou, Robust \({H}_\infty \) filtering for uncertain Markovian jump systems with mode-dependent distributed delays. Int. J. Adapt. Control Signal Process. 24(1), 83–94 (2010)

    MathSciNet  MATH  Google Scholar 

  61. J. Zhou, T. Chen, L. Xiang, Chaotic lag synchronization of coupled delayed neural networks and its applications in secure communication. Circuits, Syst., Signal Process. 24(5), 599–613 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  62. J. Zhou, T. Chen, L. Xiang, Robust synchronization of delayed neural networks based on adaptive control and parameters identification. Chaos, Solitons Fractals 27(4), 905–913 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  63. W. Zhou, H. Lu, C. Duan, Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity. Neurocomputing 72(13), 3357–3365 (2009)

    Article  Google Scholar 

  64. W. Zhou, D. Tong, Y. Gao, C. Ji, H. Su, Mode and delay-dependent adaptive exponential synchronization in pth moment for stochastic delayed neural networks with Markovian switching. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 662–668 (2012)

    Article  Google Scholar 

  65. Q. Zhu, J. Cao, Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays. Commun. Nonlinear Sci. Numer. Simul. 16(4), 2139–2159 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  66. S. Zhu, Y. Shen, Passivity analysis of stochastic delayed neural networks with Markovian switching. Neurocomputing 74(10), 1754–1761 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Sciences and Technology, Donghua University, Shanghai, China

    Wuneng Zhou & Liuwei Zhou

  2. Anyang Normal University, Anyang, China

    Jun Yang

  3. Shanghai University of Engineering Science, Shanghai, China

    Dongbing Tong

Authors
  1. Wuneng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liuwei Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongbing Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wuneng Zhou .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zhou, W., Yang, J., Zhou, L., Tong, D. (2016). Adaptive Synchronization of Neural Networks. In: Stability and Synchronization Control of Stochastic Neural Networks. Studies in Systems, Decision and Control, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47833-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-47833-2_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47832-5

  • Online ISBN: 978-3-662-47833-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation