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Non-chattering quantized control for synchronization in finite–fixed time of delayed Cohen–Grossberg-type fuzzy neural networks with discontinuous activation

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Abstract

This paper investigates the controller design problem of synchronization in finite-\(\setminus \)fixed-time of a class Cohen–Grossberg-type fuzzy neural networks (CGFNNs) with discontinuous activation function and time-varying delays. By using the Lyapunov theory and differential inclusion theory, FT synchronization condition for CGF-NNs and the upper bound of the settling time for synchronization are obtained. Moreover, the settling time of FXT synchronization, that does not depend upon the initial values, is merely calculated. A novel criterion for guaranteeing the FXT synchronization of CGFNNs is derived. Our control schema achieves system synchronization within bounded time and has an advantage in convergence rate. Numerical simulations are provided to illustrate the efficaciousness of the ideal analysis.

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References

  1. Abdurahman A, Jiang H, Teng Z (2016) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111

    Article  MathSciNet  MATH  Google Scholar 

  2. Abdurahman A, Jiang H, Hu C (2017) General decay synchronization of memristor-based Cohen-Grossberg neural networks with mixed time-delays and discontinuous activations. J Franklin Inst 354(15):7028–7052

    Article  MathSciNet  MATH  Google Scholar 

  3. Ali MS, Narayanan G, Sevgen S, Shekher V, Arik S (2019) Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects. Commun Nonlinear Sci Numerical Simul 78:104853

    Article  MathSciNet  MATH  Google Scholar 

  4. Alimi AM, Aouiti C, Assali EA (2019) Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 332:29–43

    Article  Google Scholar 

  5. Aouiti C, Assali EA (2018) Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 31(11):7781–7803

    Article  Google Scholar 

  6. Aouiti C, Assali EA (2019) Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen-Grossberg-type neural networks. Int J Adapt Control Signal Process 33(10):1457–1477

    Article  MathSciNet  MATH  Google Scholar 

  7. Aouiti C, Dridi F (2019) New results on impulsive Cohen-Grossberg neural networks. Neural Process Lett 49(3):1459–1483

    Article  MATH  Google Scholar 

  8. Aouiti C, M’hamdi MS, Chérif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46(2):487–506

    Article  Google Scholar 

  9. Aouiti C, abed Assali E, Cao J, Alsaedi A (2018) Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays. Int J Syst Sci 49(10):2202–2214

    Article  MathSciNet  Google Scholar 

  10. Aouiti C, Mhamdi MS, Chérif F, Alimi AM (2018) Impulsive generalized high-order recurrent neural networks with mixed delays: stability and periodicity. Neurocomputing 321:296–307

    Article  Google Scholar 

  11. Aouiti C, Assali EA, El Foutayeni Y (2019) Finite-time and fixed-time Synchronization of Inertial Cohen-Grossberg-Type Neural Networks with Time Varying Delays. Neural Process Lett 50(3):2407–2436

    Article  Google Scholar 

  12. Aouiti C, Assali EA, Gharbia IB, El Foutayeni Y (2019) Existence and exponential stability of piecewise pseudo almost periodic solution of neutral-type inertial neural networks with mixed delay and impulsive perturbations. Neurocomputing 357:292–309

    Article  Google Scholar 

  13. Aouiti C, Bessifi M, Li X (2020) Finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. Circuits Syst Signal Process 9:5406–5428

    Article  Google Scholar 

  14. Aquino G, Rubio JDJ, Pacheco J, Gutierrez GJ, Ochoa G, Balcazar R, Zacarias A (2020) Novel nonlinear hypothesis for the delta parallel robot modeling. IEEE Access 8:46324–46334

    Article  Google Scholar 

  15. Brockett RW, Liberzon D (2000) Quantized feedback stabilization of linear systems. IEEE Trans Autom Control 45(7):1279–1289

    Article  MathSciNet  MATH  Google Scholar 

  16. Cao J (2004) An estimation of the domain of attraction and convergence rate for Hopfield continuous feedback neural networks. Phys Lett A 325(5–6):370–374

    Article  MathSciNet  MATH  Google Scholar 

  17. Cao J, Liang J (2004) Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J Math Anal Appl 296(2):665–685

    Article  MathSciNet  MATH  Google Scholar 

  18. Chiang HS, Chen MY, Huang YJ (2019) Wavelet-based EEG processing for epilepsy detection using fuzzy entropy and associative petri net. IEEE Access 7:103255–103262

    Article  Google Scholar 

  19. Clarke FH (1990) Optimization and nonsmooth analysis (Vol. 5). Siam

  20. de Jesús Rubio J (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuzzy Syst 17(6):1296–1309

    Article  Google Scholar 

  21. de Rubio JJ (2020) Stability analysis of the modified Levenberg-Marquardt algorithm for the artificial neural network training. IEEE Transactions on Neural Networks and Learning Systems

  22. Ding W, Han M (2008) Synchronization of delayed fuzzy cellular neural networks based on adaptive control. Phys Lett A 372(26):4674–4681

    Article  MATH  Google Scholar 

  23. Ding X, Cao J, Alsaedi A, Alsaadi FE, Hayat T (2017) Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions. Neural Netw 90:42–55

    Article  MATH  Google Scholar 

  24. Dorato P (1961) Short-time stability in linear time-varying systems. Polytechnic Inst Of Brooklyn Ny Microwave Research Inst

  25. Duan L, Wei H, Huang L (2019) Finite-time synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Fuzzy Sets Syst 361:56–70

    Article  MathSciNet  MATH  Google Scholar 

  26. Filippov AF (1960) Differential equations with discontinuous right-hand side. Matematicheskii sbornik 93(1):99–128

    MathSciNet  MATH  Google Scholar 

  27. Forti M, Nistri P (2003) On global stability of Hopfield neural networks with discontinuous neuron activations. In Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS’03. (Vol. 3, pp. III-III). IEEE

  28. Hernández G, Zamora E, Sossa H, Téllez G, Furlán F (2020) Hybrid neural networks for big data classification. Neurocomputing 390:327–340

    Article  Google Scholar 

  29. Huang T (2006) Exponential stability of fuzzy cellular neural networks with distributed delay. Phys Lett A 351(1–2):48–52

    Article  MATH  Google Scholar 

  30. Jia R (2017) Finite-time stability of a class of fuzzy cellular neural networks with multi-proportional delays. Fuzzy Sets Syst 319:70–80

    Article  MathSciNet  MATH  Google Scholar 

  31. Kennedy MP, Chua LO (1988) Neural networks for nonlinear programming. IEEE Trans Circuits Syst 35(5):554–562

    Article  MathSciNet  Google Scholar 

  32. Kong F, Rajan R (2020) Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time delays. Fuzzy Sets Syst 411:105–135

    Article  MathSciNet  MATH  Google Scholar 

  33. Kong F, Zhu Q, Liang F, Nieto JJ (2019) Robust fixed-time synchronization of discontinuous Cohen-Grossberg neural networks with mixed time delays. Nonlinear Anal: Model Control 24(4):603–625

    MathSciNet  MATH  Google Scholar 

  34. Kong F, Zhu Q, Wang K, Nieto JJ (2019) Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator. J Franklin Inst 356(18):11605–11637

    Article  MathSciNet  MATH  Google Scholar 

  35. Kong F, Zhu Q, Sakthivel R (2019) Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks. Fuzzy Sets Syst 411:105–135

    Article  MATH  Google Scholar 

  36. Li C, Li Y, Ye Y (2010) Exponential stability of fuzzy Cohen-Grossberg neural networks with time delays and impulsive effects. Commun Nonlinear Sci Numer Simul 15(11):3599–3606

    Article  MathSciNet  MATH  Google Scholar 

  37. Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Franklin Inst 348(2):135–155

    Article  MathSciNet  MATH  Google Scholar 

  38. Liu X, Ho DW, Yu W, Cao J (2014) A new switching design to finite time stabilization of nonlinear systems with applications to neural networks. Neural Netw 57:94–102

    Article  MATH  Google Scholar 

  39. Liu X, Su H, Chen MZ (2015) A switching approach to designing finite-time synchronization controllers of coupled neural networks. IEEE Trans Neural Netw Learn Syst 27(2):471–482

    Article  MathSciNet  Google Scholar 

  40. Meda-Campaña JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968–31973

    Article  Google Scholar 

  41. Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    Article  MathSciNet  MATH  Google Scholar 

  42. Ratnavelu K, Manikandan M, Balasubramaniam P (2015) Synchronization of fuzzy bidirectional associative memory neural networks with various time delays. Appl Math Comput 270:582–605

    MathSciNet  MATH  Google Scholar 

  43. Song Q, Cao J (2007) Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays. IEEE Trans Syst, Man, Cybernetics, Part B Cybernetics 37(3):733–741

    Article  Google Scholar 

  44. Song G, Li T, Li Y, Lu J (2016) Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator. Nonlinear Dyn 83(1–2):305–317

    Article  MathSciNet  MATH  Google Scholar 

  45. Tang R, Yang X, Wan X (2019) Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers. Neural Netw 113:79–90

    Article  MATH  Google Scholar 

  46. Wan Y, Cao J, Wen G (2016) Quantized synchronization of chaotic neural networks with scheduled output feedback control. IEEE Trans Neural Netw Learn Syst 28(11):2638–2647

    Article  MathSciNet  Google Scholar 

  47. Wang W (2018) Finite-time synchronization for a class of fuzzy cellular neural networks with time-varying coefficients and proportional delays. Fuzzy Sets Syst 338:40–49

    Article  MathSciNet  MATH  Google Scholar 

  48. Xiao X, Zhou L, Zhang Z (2014) Synchronization of chaotic Lur’e systems with quantized sampled-data controller. Commun Nonlinear Sci Numer Simul 19(6):2039–2047

    Article  MathSciNet  MATH  Google Scholar 

  49. Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2017) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybernetics 48(10):3021–3027

    Article  Google Scholar 

  50. Yang X, Cao J (2010) Finite-time stochastic synchronization of complex networks. Appl Math Model 34(11):3631–3641

    Article  MathSciNet  MATH  Google Scholar 

  51. Yang X, Cao J (2013) Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Trans Circuits Syst I Regul Pap 60(9):2431–2439

    Article  MathSciNet  MATH  Google Scholar 

  52. Yang T, Yang LB (1996) The global stability of fuzzy cellular neural network. IEEE Trans Circuits Syst I: Fundamental Theory Appl 43(10):880–883

    Article  MathSciNet  Google Scholar 

  53. Yang X, Wu Z, Cao J (2013) Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn 73(4):2313–2327

    Article  MathSciNet  MATH  Google Scholar 

  54. Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Franklin Inst 352(10):4382–4406

    Article  MathSciNet  MATH  Google Scholar 

  55. Yang X, Cao J, Song Q, Xu C, Feng J (2017) Finite-time synchronization of coupled markovian discontinuous neural networks with mixed delays. Circuits, Syst, Signal Process 36(5):1860–1889

    Article  MATH  Google Scholar 

  56. Yang X, Lam J, Ho DW, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via nonchattering control. IEEE Trans Autom Control 62(11):5511–5521

    Article  MathSciNet  MATH  Google Scholar 

  57. Yang W, Yu W, Cao J, Alsaadi FE, Hayat T (2018) Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses. Neural Netw 98:122–153

    Article  MATH  Google Scholar 

  58. Yang X, Cao J, Xu C, Feng J (2018) Finite-time stabilization of switched dynamical networks with quantized couplings via quantized controller. Sci China Technol Sci 61(2):299–308

    Article  Google Scholar 

  59. Yang T, Yang LB, Wu CW, Chua LO (1996) Fuzzy cellular neural networks: applications. In 1996 Fourth IEEE International Workshop on Cellular Neural Networks and Their Applications Proceedings (CNNA-96) (pp. 225-230). IEEE

  60. Yang T, Yang LB, Wu CW, Chua LO (1996) Fuzzy cellular neural networks: theory. In 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96) (pp. 181-186). IEEE

  61. Yuan K, Cao J (2004) Global exponential stability of Cohen-Grossberg neural networks with multiple time-varying delays. In International Symposium on Neural Networks (pp. 78-83). Springer, Berlin, Heidelberg

  62. Zhang J, Suda Y, Komine H (2005) Global exponential stability of Cohen-Grossberg neural networks with variable delays. Phys Lett A 338(1):44–50

    Article  MATH  Google Scholar 

  63. Zhang W, Yang X, Xu C, Feng J, Li C (2017) Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters. IEEE Trans Neural Netw Learn Syst 29(8):3761–3771

    MathSciNet  Google Scholar 

  64. Zhang W, Yang S, Li C, Li Z (2019) Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control. Neural Process Lett 50(3):2073–2086

    Article  Google Scholar 

  65. Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y, Zhao H (2018) fixed-time synchronization of memristor-based fuzzy cellular neural network with time-varying delay. J Franklin Inst 355(14):6780–6809

    Article  MathSciNet  MATH  Google Scholar 

  66. Zheng M, Li L, Peng H, Xiao J, Yang Y, Zhang Y (2018) fixed-time synchronization of memristive fuzzy BAM cellular neural networks with time-varying delays based on feedback controllers. IEEE Access 6:12085–12102

    Article  Google Scholar 

  67. Zhu Q, Li X (2012) Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen-Grossberg neural networks. Fuzzy Sets Syst 203:74–94

    Article  MathSciNet  MATH  Google Scholar 

  68. Zhu Q, Cao J, Rakkiyappan R (2015) Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays. Nonlinear Dyn 79(2):1085–1098

    Article  MathSciNet  MATH  Google Scholar 

  69. Zhu X, Yang X, Alsaadi FE, Hayat T (2018) fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations. Neural Process Lett 48(2):1161–1174

    Article  Google Scholar 

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Authors and Affiliations

  1. Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Mayssa Bessifi

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  1. Chaouki Aouiti
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  2. Mayssa Bessifi
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Correspondence to Chaouki Aouiti.

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Aouiti, C., Bessifi, M. Non-chattering quantized control for synchronization in finite–fixed time of delayed Cohen–Grossberg-type fuzzy neural networks with discontinuous activation. Neural Comput & Applic 33, 16557–16576 (2021). https://doi.org/10.1007/s00521-021-06253-7

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