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Finite-time stabilization of uncertain delayed-hopfield neural networks with a time-varying leakage delay via non-chattering control

Abstract

This article is concerned with the finite-time stabilization (FTSB) of a class of delayed-Hopfield neural networks with a time-varying delay in the leakage term in the presence of parameter uncertainties. To accomplish the target of FTSB, two new finite-time controllers are designed for uncertain delayed-Hopfield neural networks with a time-varying delay in the leakage term. By utilizing the finite-time stability theory and the Lyapunov-Krasovskii functional (LKF) approach, some sufficient conditions for the FTSB of these neural networks are established. These conditions, which can be used for the selection of control parameters, are in the form of linear matrix inequalities (LMIs) and can be numerically checked. Additionally, an upper bound of the settling time was estimated. Finally, our theoretical results are further substantiated by two numerical examples with graphical illustrations to demonstrate the effectiveness of the results.

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References

  1. Mathiyalagan K, Hongye Su K, Peng Shi K, et al. Exponential H filtering for discrete-time switched neural networks with random delays. IEEE Trans Cybern, 2015, 45: 676–687

    Article  Google Scholar 

  2. Mathiyalagan K, Anbuvithya R, Sakthivel R, et al. Non-fragile H synchronization of memristor-based neural networks using passivity theory. Neural Networks, 2016, 74: 85–100

    Article  MATH  Google Scholar 

  3. Nitta T. Orthogonality of decision boundaries in complex-valued neural networks. Neural Computation, 2004, 16: 73–97

    Article  MATH  Google Scholar 

  4. Aouiti C, Alimi A M, Karray F, et al. The design of beta basis function neural network and beta fuzzy systems by a hierarchical genetic algorithm. Fuzzy Sets Syst, 2005, 154: 251–274

    MathSciNet  Article  MATH  Google Scholar 

  5. Aouiti C, Alimi A M, Maalej A. A genetic-designed beta basis function neural network for multi-variable functions approximation. Syst Anal Model Simul, 2002, 42: 975–1009

    Article  MATH  Google Scholar 

  6. Forti M, Nistri P, Quincampoix M. Generalized neural network for nonsmooth nonlinear programming problems. IEEE Trans Circuits Syst I, 2004, 51: 1741–1754

    MathSciNet  Article  MATH  Google Scholar 

  7. Li X D, Song S J. Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learning Syst, 2013, 24: 868–877

    Article  Google Scholar 

  8. Aouiti C. Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn, 2016, 10: 573–591

    Article  Google Scholar 

  9. Aouiti C, Mhamdi M S, Touati A. Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett, 2017, 45: 121–140

    Article  Google Scholar 

  10. Aouiti C, Coirault P, Miaadi F, et al. Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing, 2017, 260: 378–392

    Article  Google Scholar 

  11. Li X, Cao J. An impulsive delay inequality involving unbounded timevarying delay and applications. IEEE Trans Automat Contr, 2017, 62: 3618–3625

    Article  MATH  Google Scholar 

  12. Li X, Ho D, Cao J. Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica, 2019, 99: 361–368

    MathSciNet  Article  MATH  Google Scholar 

  13. Li X, Bohner M, Wang C K. Impulsive differential equations: Periodic solutions and applications. Automatica, 2015, 52: 173–178

    MathSciNet  Article  MATH  Google Scholar 

  14. Li X, Zhang X, Song S. Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica, 2017, 76: 378–382

    MathSciNet  Article  MATH  Google Scholar 

  15. Li X, Fu X. Effect of leakage time-varying delay on stability of nonlinear differential systems. J Franklin Institute, 2013, 350: 1335–1344

    MathSciNet  Article  MATH  Google Scholar 

  16. Stamova I, Stamov T, Li X. Global exponential stability of a class of impulsive cellular neural networks with supremums. Int J Adapt Control Signal Process, 2014, 28: 1227–1239

    MathSciNet  Article  MATH  Google Scholar 

  17. Aouiti C, Miaadi F. Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays. Neural Comp Appl, 2018, doi: https://doi.org/10.1007/s00521-017-3314-z

    Google Scholar 

  18. Hu V P H, Fan M L, Su P, et al. Leakage-delay analysis of ultra-thinbody GeOI devices and logic circuits. In: Proceedings of the 2011 International Symposium on VLSI Technology, Systems and Applications. Taiwan: IEEE, 2011. 1–2

    Google Scholar 

  19. Zhang H, Wang Z, Liu D. A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learning Syst, 2014, 25: 1229–1262

    Article  Google Scholar 

  20. Li X, Song S. Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans Automat Contr, 2017, 62: 406–411

    MathSciNet  Article  MATH  Google Scholar 

  21. Li Y, Zeng Z, Wen S. Asymptotic stability analysis on nonlinear systems with leakage delay. J Franklin Institute, 2016, 353: 757–779

    MathSciNet  Article  MATH  Google Scholar 

  22. Li X, Wu J. Sufficient stability conditions of nonlinear differential systems under impulsive control with state-dependent delay. IEEE Trans Automat Contr, 2018, 63: 306–311

    MathSciNet  Article  MATH  Google Scholar 

  23. Aouiti C. Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Compu Appl, 2018, 29: 477–495

    Article  Google Scholar 

  24. Aouiti C, Mhamdi M S, Cao J, et al. Piecewise pseudo almost periodic solution for impulsive generalised high-order hopfield neural networks with leakage delays. Neural Process Lett, 2017, 45: 615–648

    Article  Google Scholar 

  25. Li X, Wu J. Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica, 2016, 64: 63–69

    MathSciNet  Article  MATH  Google Scholar 

  26. Liu X, Jiang N, Cao J, et al. Finite-time stochastic stabilization for BAM neural networks with uncertainties. J Franklin Institute, 2013, 350: 2109–2123

    MathSciNet  Article  MATH  Google Scholar 

  27. Wu Y, Cao J, Alofi A, et al. Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay. Neural Networks, 2015, 69: 135–143

    Article  MATH  Google Scholar 

  28. Cao J, Huang D S, Qu Y. Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals, 2005, 23: 221–229

    MathSciNet  Article  MATH  Google Scholar 

  29. Ji C, Zhang H G, Wei Y. LMI approach for global robust stability of Cohen-Grossberg neural networks with multiple delays. Neurocomputing, 2008, 71: 475–485

    Article  Google Scholar 

  30. Zhang H G, Wang Y C. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw, 2008, 19: 366–370

    Article  Google Scholar 

  31. Aouiti C, Miaadi F. Finite-time stabilization of neutral hopfield neural networks with mixed delays. Neural Proces Lett, 2018, 48: 1645–1669

    Article  Google Scholar 

  32. Moulay E, Perruquetti W. Finite time stability and stabilization of a class of continuous systems. J Math Anal Appl, 2006, 323: 1430–1443

    MathSciNet  Article  MATH  Google Scholar 

  33. Haimo V T. Finite time controllers. SIAM J Control Optim, 1986, 24: 760–770

    MathSciNet  Article  MATH  Google Scholar 

  34. Bhat S P, Bernstein D S. Lyapunov analysis of finite-time differential equations. In: Proceedings of the 1995 American Control Conference. IEEE, 1995. 831–1832

  35. Bhat S P, Bernstein D S. Finite-time stability of homogeneous systems. In: Proceedings of the 1997 American Control Conference. IEEE, 1997. 2513–2514

    Google Scholar 

  36. Bhat S P, Bernstein D S. Finite-time stability of continuous autonomous systems. SIAM J Control Optim, 2000, 38: 751–766

    MathSciNet  Article  MATH  Google Scholar 

  37. Moulay E, Dambrine M, Yeganefar N, et al. Finite-time stability and stabilization of time-delay systems. Syst Control Lett, 2008, 57: 561–566

    MathSciNet  Article  MATH  Google Scholar 

  38. Perruquetti W, Floquet T, Moulay E. Finite-time observers: Application to secure communication. IEEE Trans Automat Contr, 2008, 53: 356–360

    MathSciNet  Article  MATH  Google Scholar 

  39. Du H, Li S, Qian C. Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans Automat Contr, 2011, 56: 2711–2717

    MathSciNet  Article  MATH  Google Scholar 

  40. Mathiyalagan K, Balachandran K. Finite-time stability of fractional-order stochastic singular systems with time delay and white noise. Complexity, 2016, 21: 370–379

    MathSciNet  Article  Google Scholar 

  41. Huang J, Li C, Huang T, et al. Finite-time lag synchronization of delayed neural networks. Neurocomputing, 2014, 139: 145–149

    Article  Google Scholar 

  42. Mathiyalagan K, Park J H, Sakthivel R. Finite-time boundedness and dissipativity analysis of networked cascade control systems. Nonlinear Dyn, 2016, 84: 2149–2160

    MathSciNet  Article  MATH  Google Scholar 

  43. Liu X, Ho D W C, Yu W, et al. A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks. Neural Networks, 2014, 57: 94–102

    Article  MATH  Google Scholar 

  44. Liu X, Park J H, Jiang N, et al. Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Networks, 2014, 52: 25–32

    Article  MATH  Google Scholar 

  45. Shen H, Park J H, Wu Z G. Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn, 2014, 77: 1709–1720

    MathSciNet  Article  MATH  Google Scholar 

  46. Shen J, Cao J. Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn, 2011, 5: 373–385

    Article  Google Scholar 

  47. Wang L, Shen Y. Finite-time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller. IEEE Trans Neural Netw Learning Syst, 2015, 26: 2914–2924

    MathSciNet  Article  Google Scholar 

  48. Wang L, Shen Y, Ding Z. Finite time stabilization of delayed neural networks. Neural Networks, 2015, 70: 74–80

    Article  MATH  Google Scholar 

  49. Wang L, Shen Y, Sheng Y. Finite-time robust stabilization of uncertain delayed neural networks with discontinuous activations via delayed feedback control. Neural Networks, 2016, 76: 46–54

    Article  MATH  Google Scholar 

  50. Wu R, Lu Y, Chen L. Finite-time stability of fractional delayed neural networks. Neurocomputing, 2015, 149: 700–707

    Article  Google Scholar 

  51. Yang S, Li C, Huang T. Finite-time stabilization of uncertain neural networks with distributed time-varying delays. Neural Comput Applic, 2017, 28: 1155–1163

    Article  Google Scholar 

  52. Lv X, Li X. Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications. ISA Trans, 2017, 70: 30–36

    Article  Google Scholar 

  53. Zhou J, Lu J, Lü J. Pinning adaptive synchronization of a general complex dynamical network. Automatica, 2008, 44: 996–1003

    MathSciNet  Article  MATH  Google Scholar 

  54. Liu T, Hill D J, Zhao J. Synchronization of dynamical networks by network control. IEEE Trans Automat Contr, 2012, 57: 1574–1580

    MathSciNet  Article  MATH  Google Scholar 

  55. Zuo Z, Tie L. Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci, 2016, 47: 1366–1375

    MathSciNet  Article  MATH  Google Scholar 

  56. Wan Y, Cao J, Wen G, et al. Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks. Neural Networks, 2016, 73: 86–94

    Article  MATH  Google Scholar 

  57. Yang X, Ho D W C, Lu J, et al. Finite-time cluster synchronization of T-S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst, 2015, 23: 2302–2316

    Article  Google Scholar 

  58. Hamayun M T, Edwards C, Alwi H. Fault Tolerant Control Schemes Using Integral Sliding Modes. Cham: Springer International Publishing, 2016. 17–37

    Book  MATH  Google Scholar 

  59. Hale J K. Theory of Functional Differential Equations. New York: Springer, 1977. 36–56

    Book  Google Scholar 

  60. Boyd S, El Ghaoui L, Feron, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 1994. 20–78

    Book  MATH  Google Scholar 

  61. Hale J K. Ordinary differential equations. Pure Appl Math, 1980, 20: 36–56

    Google Scholar 

  62. Cai Z W, Huang L H. Finite-time synchronization by switching state-feedback control for discontinuous CohenGrossberg neural networks with mixed delays. Int J Machine Learn and Cybernet, 2018, 9: 1683–1695

    Article  Google Scholar 

  63. Yang X. Can neural networks with arbitrary delays be finite-timely synchronized? Neurocomputing, 2014, 143: 275–281

    Article  Google Scholar 

  64. Zhou C, Zhang W, Yang X, et al. Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations. Neural Process Lett, 2017, 46: 271–291

    Article  Google Scholar 

  65. Li Y, Yang X, Shi L. Finite-time synchronization for competitive neural networks with mixed delays and non-identical perturbations. Neurocomputing, 2016, 185: 242–253

    Article  Google Scholar 

  66. Shi L, Yang X, Li Y, et al. Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn, 2016, 83: 75–87

    MathSciNet  Article  MATH  Google Scholar 

  67. Léchappé V, Moulay E, Plestan F, et al. New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 2015, 52: 179–184

    MathSciNet  Article  MATH  Google Scholar 

  68. Lechappe V, Rouquet S, Gonzalez A, et al. Delay estimation and predictive control of uncertain systems with input delay: Application to a DC motor. IEEE Trans Ind Electron, 2016, 63: 5849–5857

    Article  Google Scholar 

  69. Hu C, Yu J, Chen Z, et al. Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Networks, 2017, 89: 74–83

    Article  Google Scholar 

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Correspondence to XiaoDi Li.

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Aouiti, C., Li, X. & Miaadi, F. Finite-time stabilization of uncertain delayed-hopfield neural networks with a time-varying leakage delay via non-chattering control. Sci. China Technol. Sci. 62, 1111–1122 (2019). https://doi.org/10.1007/s11431-017-9284-y

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  • DOI: https://doi.org/10.1007/s11431-017-9284-y

Keywords

  • neural networks
  • finite-time stabilization
  • parametric uncertainties
  • leakage delay
  • Lyapunov-Krasovskii functional
  • LMI