Abstract
This paper addresses the intermittent pinning synchronization problem of spatial diffusion coupled reaction–diffusion neural networks (RDNNs). Initially, the synchronization error signals are quantized before transmission to save both channel resource and control cost. Subsequently, utilizing intermittent pinning control scheme, only a small fraction of network nodes are selected to be controlled in various time periods, which further reduces the control cost. On the basis of the constructed controller, sufficient conditions that guarantee the synchronization of the coupled RDNNs are derived via Lyapunov direct method. Finally, the efficacy of the developed control approach is demonstrated by numerical simulation studies of three examples.
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Shen H, Zhu Y, Zhang L, Park JH (2016) Extended dissipative state estimation for Markov jump neural networks with unreliable links. IEEE Trans Neural Netw Learn Syst 28(2):346–358
Abd Elazim S, Ali E (2016) Load frequency controller design via BAT algorithm for nonlinear interconnected power system. Int J Electr Power Energ Syst 77:166–177
Chen L, Liu C, Wu R, He Y, Chai Y (2016) Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Comput Appl 27(3):549–556
Li Q, Shen B, Liu Y, Huang T (2017) Event-triggered \({H}_\infty\) state estimation for discrete-time neural networks with mixed time delays and sensor saturations. Neural Comput Appl 28(12):3815–3825
Abd Elazim S, Ali E (2016) Imperialist competitive algorithm for optimal STATCOM design in a multimachine power system. Int J Electr Power Energ Syst 76:136–146
Abd Elazim S, Ali E (2018) Load frequency controller design of a two-area system composing of PV grid and thermal generator via firefly algorithm. Neural Comput Appl 30(2):607–616
Ali E, Elazim SA (2018) Mine blast algorithm for environmental economic load dispatch with valve loading effect. Neural Comput Appl 30(1):261–270
Jutras MJ, Buffalo EA (2010) Synchronous neural activity and memory formation. Curr Opin Neurobiol 20(2):150–155
Song Q, Liu F, Wen G, Cao J, Yang X (2017) Distributed position-based consensus of second-order multiagent systems with continuous/intermittent communication. IEEE Trans Cybern 47(8):1860–1871
Li H, Liao X, Huang T, Wang Y, Han Q, Dong T (2014) Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies. Inf Sci 259:25–35
He W, Chen G, Han QL, Du W, Cao J, Qian F (2017) Multiagent systems on multilayer networks: synchronization analysis and network design. IEEE Trans Syst Man Cybern Syst 47(7):1655–1667
Shen H, Park JH, Wu ZG (2014) Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn 77(4):1709–1720
Song S, Song X, Balsera IT (2017) Mixed \({H}_\infty\) and passive projective synchronization for fractional-order memristor-based neural networks with time delays via adaptive sliding mode control. Mod Phys Lett B 31(14):1750160
Zhou W, Zhu Q, Shi P, Su H, Fang J, Zhou L (2014) Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters. IEEE Trans Cybern 44(12):2848–2860
Shen H, Wu Z, Zhang Z, Park JH (2014) Non-fragile mixed \({\mathscr {H}}_{\infty }\)/\({\mathscr {L}}_2-{\mathscr {L}}_{\infty }\) synchronisation control for complex networks with Markov jumping-switching topology under unreliable communication links. IET Control Theory Appl 8(18):2207–2218
Su L, Shen H (2016) Fault-tolerant mixed \({H}_{\infty }\)/passive synchronization for delayed chaotic neural networks with sampled-data control. Complexity 21(6):246–259
Yu W, Chen G, Lü J (2009) On pinning synchronization of complex dynamical networks. Automatica 45(2):429–435
Guan Z, Liu Z, Feng G, Wang Y (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circuits Syst I Regular Papers 57(8):2182–2195
Zhang G, Shen Y (2014) Exponential synchronization of delayed memristor-based chaotic neural networks via periodically intermittent control. Neural Netw 55:1–10
Mei J, Jiang M, Wu Z, Wang X (2015) Periodically intermittent controlling for finite-time synchronization of complex dynamical networks. Nonlinear Dyn 79(1):295–305
Liu X, Chen T (2015) Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans Autom Control 60(12):3316–3321
Gao J, Cao J (2017) Aperiodically intermittent synchronization for switching complex networks dependent on topology structure. Adv Differ Equ 2017(1):244
Zhang W, Li C, Huang T, Xiao M (2015) Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control. Neural Netw 71:105–111
Ali MS, Zhu Q, Pavithra S, Gunasekaran N (2018) A study on (Q, S, R)-\(\gamma\)-dissipative synchronisation of coupled reaction-diffusion neural networks with time-varying delays. Int J Syst Sci 49(4):755–765
Wang J, Zhang X, Wu H, Huang T, Wang Q (2018) Finite-time passivity and synchronization of coupled reaction-diffusion neural networks with multiple weights. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2842437
Rakkiyappan R, Dharani S (2017) Sampled-data synchronization of randomly coupled reaction-diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach. Neural Comput Appl 28(3):449–462
Wang J, Wu H, Huang T, Ren S, Wu J (2017) Pinning control for synchronization of coupled reaction-diffusion neural networks with directed topologies. IEEE Trans Syst Man Cybern Syst 46(8):1109–1120
Hu C, Jiang H, Teng Z (2010) Impulsive control and synchronization for delayed neural networks with reaction–diffusion terms. IEEE Trans Neural Netw 21(1):67–81
Liu X, Zhang K, Xie WC (2017) Pinning impulsive synchronization of reaction-diffusion neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 28(5):1055–1067
Ozcan N, Ali MS, Yogambigai J, Zhu Q, Arik S (2018) Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction-diffusion terms via sampled-data control. J Frankl Inst 355(3):1192–1216
Yin S, Hao Z, Zeng Z (2017) Synchronization of reaction–diffusion neural networks with Dirichlet boundary conditions and infinite delays. IEEE Trans Cybern 47(10):3005–3017
Liu X, Chen Z, Zhou L (2017) Synchronization of coupled reaction-diffusion neural networks with hybrid coupling via aperiodically intermittent pinning control. J Frankl Inst 354(15):7053–7076
Mei J, Jiang M, Wang B, Liu Q, Xu W, Liao T (2014) Exponential p-synchronization of non-autonomous Cohen-Grossberg neural networks with reaction-diffusion terms via periodically intermittent control. Neural Process Lett 40(2):103–126
Lu B, Jiang H, 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
Zhang R, Zeng D, Park H, Liu JY, Zhong S (2018) Quantized sampled-data control for synchronization of inertial neural networks with heterogeneous time-varying delays, IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2836339.
Feng Y, Xiong X, Tang R, Yang X (2018) Exponential synchronization of inertial neural networks with mixed delays via quantized pinning control. Neurocomputing 310:165–171
Yang X, Song Q, Cao J, Lu J (2018) Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2853650
Lu J (2008) Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fractals 35(1):116–125
Wang Y, Xie L, de Souza CE (1992) Robust control of a class of uncertain nonlinear systems. Syst Control Lett 19(2):139–149
Wang J, Wu H (2012) Local and global exponential output synchronization of complex delayed dynamical networks. Nonlinear Dyn 67(1):497–504
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(1):485–500
Shanmugam L, Mani P, Rajan R, Joo YH (2018) Adaptive synchronization of reaction-diffusion neural networks and its application to secure communication. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2018.2877410
Chen W, Luo S, Zheng W (2016) Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption. IEEE Trans Neural Netw Learn Syst 27(12):2696–2710
Yang C, Li X, Qiu J (2018) Output synchronization control with input constraint of complex networks with reaction-diffusion terms. Neural Comput Appl 30(11):3295–3302
Acknowledgements
Project is supported by National Natural Science Foundation of China (No. U1604146), Science and Technology Research Project in Henan Province (No. 162102410024), Foundation for the University Technological Innovative Talents of Henan Province (No. 18HASTIT019). The authors declare that there is no conflict of interest regarding the publication of this paper.
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Song, X., Wang, M., Song, S. et al. Intermittent pinning synchronization of reaction–diffusion neural networks with multiple spatial diffusion couplings. Neural Comput & Applic 31, 9279–9294 (2019). https://doi.org/10.1007/s00521-019-04254-1
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DOI: https://doi.org/10.1007/s00521-019-04254-1