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Event-triggered synchronization of uncertain delayed generalized RDNNs

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Abstract

This paper investigates the exponential synchronization analysis of master–slave chaotic uncertain delayed generalized reaction–diffusion neural networks (GRDNNs) with event-triggered control scheme. A delay GRDNNs system model for the analysis is constructed by investigating the effect of the network transmission delay. By constructing a novel Lyapunov–Krasovskii functional and using a delay system approach for designing event-triggered controllers and some inequality techniques like Jensen’s inequality, Wirtinger’s inequality and Halanay’s inequality, the criteria are obtained for the event-triggered synchronization analysis and control synthesis of delayed GRDNNs. The synchronization criteria are formulated in terms of linear matrix inequalities. Finally, we conclude that the slave systems synchronize with the master systems. Two examples show the proposed theoretical results are feasible and effective.

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References

  • Chen S, Song G, Zheng B, Li T (2019) Finite-time synchronization of coupled reaction–diffusion neural systems via intermittent control. Automatica 109:108564

    MathSciNet  MATH  Google Scholar 

  • Chen J, Chen B, Zeng Z (2021) Synchronization in multiple neural networks with delay and disconnected switching topology via event-triggered impulsive control strategy. IEEE Trans Ind Electron 68(3):2491–2500

    Google Scholar 

  • Court JR, Demetriou MA, Gatsonis NA (2012) Spatial gradient measurement through length scale estimation for the tracking of a gaseous source. In: American control conference, pp 2984–2989

  • Fan Y, Huang X, Shen H, Cao J (2019) Switching event-triggered control for global stabilization of delayed memristive neural networks: an exponential attenuation scheme. Neural Netw 117:216–224

    MATH  Google Scholar 

  • Fei Z, Guan C, Gao H (2017) Exponential synchronization of networked chaotic delayed neural network by a hybrid event trigger scheme. IEEE Trans Neural Netw Learn Syst 99:1–10

    Google Scholar 

  • Fridman E, Blighovsky A (2012) Robust sampled-data control of a class of semilinear parabolic systems. Automatica 48(2012):826–836

    MathSciNet  MATH  Google Scholar 

  • Gan Q, Liu T, Liu C, Lv T (2016) Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms. Nonlinear Analy Modell Control 21(3):379–399

    MathSciNet  MATH  Google Scholar 

  • Gu K, Kharitonov V, Chen J (2003) Stability of time-delay systems. Birkhauser, Boston

    MATH  Google Scholar 

  • Halanay A (1966) Differential equations: stability, oscillations, time lags. Academic Press, New York

    MATH  Google Scholar 

  • Hardy GH, Littlewood JE, Polya G (1988) Inequalities. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • He Y, Liu G, Rees D (2007) New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans Neural Netw 18(1):310–314

    Google Scholar 

  • He W, Luo T, Tang Y, Du W, Tian Y, Qian F (2019) Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy. IEEE Trans Neural Netw Learn Syst 31:3334–3345

    MathSciNet  Google Scholar 

  • Huang Y, Liu Y (2019) Switching event-triggered control for a class of uncertain nonlinear systems. Automatica 108:108471

    MathSciNet  Google Scholar 

  • Kwon OM, Park MJ, Lee SM, Park JH, Cha EJ (2013) Stability for neural networks with time-varying delays via some new approaches. IEEE Trans Neural Netw Learn Syst 24(2):181–193

    Google Scholar 

  • Kwon OM, Lee SH, Park MJ, Lee SM (2020) Augmented zero equality approach to stability for linear systems with time-varying delay. Appl Math Comput 381:125329. https://doi.org/10.1016/j.amc.2020.125329

    Article  MathSciNet  MATH  Google Scholar 

  • Li C, Liao X, Zhang R (2004) Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Phys Lett A 328(6):452–462

    MATH  Google Scholar 

  • Li T, Guo L, Sun C, Lin C (2008) Further results on delay-dependent stability criteria of neural networks with time-varying delays. IEEE Trans Neural Netw 19(4):726–730

    Google Scholar 

  • Li J, Zhang W, Chen M (2013) Synchronization of delayed reaction–diffusion neural networks via an adaptive learning control approach. Comput Math Appl 65:1775–1785

    MathSciNet  MATH  Google Scholar 

  • Li L, Zou W, Fei S (2019) Event-triggered synchronization of delayed neural networks with actuator saturation using quantized measurements. J Franklin Inst 356:6433–6459

    MathSciNet  MATH  Google Scholar 

  • Liang J, Cao J (2006) A based-on LMI stability criterion for delayed recurrent neural networks. Chaos Solitons Fractals 28(1):154–160

    MathSciNet  MATH  Google Scholar 

  • Liao X, Wong K, Wu Z, Chen G (2001) Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Trans Circuits Syst I 48(11):1355–1359

    MathSciNet  MATH  Google Scholar 

  • Liu Y, Wang Z, Liang J, Liu X (2009) stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode dependent time delays. IEEE Trans Neural Netw 20(7):1102–1116

    Google Scholar 

  • Liu Y, Lee SM, Kwon OM, Park JH (2015) New approach to stability criteria for generalized neural networks with interval time varying delays. Neurocomputing 149:1544–1551

    Google Scholar 

  • Lu B-L, Jiang H-J, Hu C, Abdurahman A (2018) Synchronization of hybrid coupled reaction-diffusion neural networks with time delays via generalized intermittent control with spacial sampled-data. Neural Netw 105:75–87

    MATH  Google Scholar 

  • Park PG, Ko JW, Jeong C (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47(1):235–238

    MathSciNet  MATH  Google Scholar 

  • Pecora LM, Carroll T-L (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–825

    MathSciNet  MATH  Google Scholar 

  • Rakkiyappan R, Dharani S, Zhu Q (2015) Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller. Nonlinear Dyn 79:485–500

    MathSciNet  MATH  Google Scholar 

  • Saravanakumar R, Syed Ali M, Ahn CK, Karimi HR, Shi P (2017) Stability of Markovian jump generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw Learn Syst 8:1840–1850

    MathSciNet  Google Scholar 

  • Selivanov A, Fridman E (2016) Distributed event-triggered control of diffusion semilinear PDEs. Automatica 68:344–351

    MathSciNet  MATH  Google Scholar 

  • Selivanov A, Fridman E (2016) Event-triggered $H_{\infty}$ control: a switching approach. IEEE Trans Autom Control 61(10):3221–3226

    MathSciNet  Google Scholar 

  • Senana S, Alib MS, Vadivelb R, Arik S (2017) Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays. Neural Netw 86:32–41

    Google Scholar 

  • Sheng Y, Zeng Z (2018) Impulsive synchronization of stochastic reaction–diffusion neural networks with mixed time delays. Neural Netw 103:83–93

    MATH  Google Scholar 

  • Smagina Y, Sheintuch M (2006) Using Lyapunov’s direct method for wave suppression in reactive systems. Syst Control Lett 7(55):566–572

    MathSciNet  MATH  Google Scholar 

  • Syed Ali M, Saravanakumar R, Arik S (2015) Delay-dependent stability criteria of uncertain Markovian jump neural networks with discrete interval and distributed time-varying delays. Neurocomputing 158:167–173

    Google Scholar 

  • Vadivel R, Syed Ali M, Joo YH (2020) Drive-response synchronization of uncertain Markov jump generalized neural networks with interval time varying delays via decentralized event-triggered communication scheme. J Franklin Inst. https://doi.org/10.1016/j.jfranklin.2020.05.004

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Wang JL, Wu HN, Huang T, Ren SY, Wu J (2017) Pinning control for synchronization of coupled reaction-diffusion neural networks with directed topologies. IEEE Tran Syst Man Cybern Syst 46(8):1109–1120

    Google Scholar 

  • Wang C, He Y, Lin W (2021) Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method. Appl Math Comput 391:125631

    MathSciNet  MATH  Google Scholar 

  • Wen S, Zeng Z, Chen MZQ, Huang T (2017) Synchronization of switched neural networks with communication delays via the event-triggered control. IEEE Trans Neural Netw Learn Syst 28(10):2334–2343

    MathSciNet  Google Scholar 

  • Wu Y, Cao J, Li Q, Alsaedi A, Alsaadi FE (2017) Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching. Neural Netw 85:128–139

    MATH  Google Scholar 

  • Xie X, Liu X, Xu H, Luo X, Liu G (2019) Synchronization of coupled reaction-diffusion neural networks: delay-dependent pinning impulsive control. Commun Nonlinear Sci Numer Simul 79:104905

    MathSciNet  MATH  Google Scholar 

  • Xu Z, Qiao H, Peng J (2004) A comparative study on two modeling approaches in neural networks. Neural Netw 17:73–85

    MATH  Google Scholar 

  • Yao Z, El-Farra NH (2013) Resource-aware model predictive control of spatially distributed processes using event-triggered communication. In: 52nd IEEE conference on decision and control, pp 3726–3731

  • Yue D, Tian E, Han Q-L (2013) A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans Autom Control 58(2):475–481

    MathSciNet  MATH  Google Scholar 

  • Zeng H-B, Park JH, Zhang C-F, Wang W (2015) Stability and dissipativity analysis of static neural networks with interval time varying delay. J Franklin Inst 352(3):1284–1295

    MathSciNet  MATH  Google Scholar 

  • Zhang X, Han Q (2011) Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw 22:1180–1192

    Google Scholar 

  • Zhang C-K, He Y, Jiang L, Wu QH, Wu M (2014) Delay dependent stability criteria for generalized neural networks with two delay components. IEEE Trans Neural Netw Learn Syst 25(7):1263–1276

    Google Scholar 

  • Zhang W, Li J, Xing K, Ding C (2016) Synchronization for distributed parameter NNs with mixed delays via sampled-data control. Neurocomputing 175:265–277

    Google Scholar 

  • Zhang H, Liu Z, Huang G-B, Wang Z (2010) Novel weighting delay-based stability criteria for recurrent neural networks with time varying delay. IEEE Trans Neural Netw 21(1):91–106

    Google Scholar 

Download references

Acknowledgements

This work is partially supported by the National Natural Science Foundation of China under Grants No. 61573013, the Special research projects in Shaanxi Province Department of Education under Grant No. 17JK0824 and Young and middle-aged top talents projects of Xianyang Normal University under Grant No. XSYBJ201801.

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Authors and Affiliations

  1. Institute of Nonlinear Science, Xianyang Normal University, Xianyang, 712000, People’s Republic of China

    Weiyuan Zhang

  2. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Junmin Li & Xinyu Zhang

  3. State Key Laboratory for Manufacturing Systems Engineering, and Systems Engineering Institute, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Keyi Xing & Rui Zhang

  4. State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Rui Zhang

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  1. Weiyuan Zhang
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Correspondence to Weiyuan Zhang.

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Zhang, W., Li, J., Xing, K. et al. Event-triggered synchronization of uncertain delayed generalized RDNNs. Soft Comput 25, 13243–13261 (2021). https://doi.org/10.1007/s00500-021-06166-6

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