Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

Chengbo Yi; Rui Guo; Jiayi Cai; Xiaohu Yan; Chengbo Yi; Rui Guo; Jiayi Cai; Xiaohu Yan

doi:10.3934/math.20231279

AIMS Mathematics

2023, Volume 8, Issue 10: 25060-25078. doi: 10.3934/math.20231279

Previous Article Next Article

Research article Special Issues

Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

Chengbo Yi ¹,
Rui Guo ^{2
,
,},
Jiayi Cai ^{3
,
,},
Xiaohu Yan ¹

1.
Industrial Training Centre, Shenzhen Polytechnic, Shenzhen 518055, China
2.
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
3.
School of Mathematics and Statistics, Guizhou University of Finance and Economies, Guizhou 550025, China

Received: 01 July 2023 Revised: 07 August 2023 Accepted: 20 August 2023 Published: 28 August 2023
MSC : 34D06, 92B20, 93D05

In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.
- event-triggered impulsive control,
- pinning control,
- dynamical neural networks,
- hybrid delays,
- exponential synchronization
Citation: Chengbo Yi, Rui Guo, Jiayi Cai, Xiaohu Yan. Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control[J]. AIMS Mathematics, 2023, 8(10): 25060-25078. doi: 10.3934/math.20231279

Related Papers:

Abstract

In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.

References

[1]	V. I. Krinsky, V. N. Biktashev, I. R. Efimov, Autowave principles for parallel image processing, Phys. D, 49 (1991), 247–253. https://doi.org/10.1016/0167-2789(91)90213-S doi: 10.1016/0167-2789(91)90213-S
[2]	Q. X. Xie, G. R. Chen, E. M. Bollt, Hybrid chaos synchronization and its application in information processing, Math. Comput. Model., 35 (2002), 145–163. https://doi.org/10.1016/S0895-7177(01)00157-1 doi: 10.1016/S0895-7177(01)00157-1
[3]	S. Dashkovskiy, M. Kosmykov, A. Mironchenko, L. Naujok, Stability of interconnected impulsive systems with and without time delays, using lyapunov methods, Nonlinear Anal. Hybrid Syst., 6 (2012), 899–915. https://doi.org/10.1016/j.nahs.2012.02.001 doi: 10.1016/j.nahs.2012.02.001
[4]	X. D. Li, D. W. C. Ho, J. D. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368. https://doi.org/10.1016/j.automatica.2018.10.024 doi: 10.1016/j.automatica.2018.10.024
[5]	F. Q. Yao, J. D. Cao, L. Qiu, P. Cheng, Exponential stability analysis for stochastic delayed differential systems with impulsive effects: Average impulsive interval approach, Asian J. Control, 19 (2017), 74–86. https://doi.org/10.1002/asjc.1320 doi: 10.1002/asjc.1320
[6]	J. Q. Lu, D. W. C. Ho, J. D. Cao, A unified synchronization criterion for impulsive dynamical networks, Automatica, 46 (2010), 1215–1221. https://doi.org/10.1016/j.automatica.2010.04.005 doi: 10.1016/j.automatica.2010.04.005
[7]	J. Q. Lu, D. W. C. Ho, J. D. Cao, J. Kurths, Single impulsive controller for globally exponential synchronization of dynamical networks, Nonlinear Anal. Real World Appl., 14 (2013), 581–593. https://doi.org/10.1016/j.nonrwa.2012.07.018 doi: 10.1016/j.nonrwa.2012.07.018
[8]	T. P. Chen, X. W. Liu, W. L. Lu, Pinning complex networks by a single controller, IEEE Trans. Circuits Syst. I. Regul. Pap., 54 (2007), 1317–1326. https://doi.org/10.1109/TCSI.2007.895383 doi: 10.1109/TCSI.2007.895383
[9]	J. Q. Lu, Z. D. Wang, J. D. Cao, D. W. C. Ho, J. Kurths, Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay, Internat. J. Bifur. Chaos, 22 (2012), 1250176. https://doi.org/10.1142/S0218127412501763 doi: 10.1142/S0218127412501763
[10]	Z. H. Guan, Z. W. Liu, G. Feng, Y. W. Wang, Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control, IEEE Trans. Circuits Syst. I. Regul. Pap., 57 (2010), 2182–2195. https://doi.org/10.1109/TCSI.2009.2037848 doi: 10.1109/TCSI.2009.2037848
[11]	D. H. Ji, S. C. Jeong, J. H. Park, S. M. Lee, S. C. Won, Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Appl. Math. Comput., 218 (2012), 4872–4880. https://doi.org/10.1016/j.amc.2011.10.051 doi: 10.1016/j.amc.2011.10.051
[12]	L. Ding, Q. L. Han, X. H. Ge, X. M. Zhang, An overview of recent advances in event-triggered consensus of multiagent systems, IEEE T. Cybernetics, 48 (2018), 1110–1123. https://doi.org/10.1109/TCYB.2017.2771560 doi: 10.1109/TCYB.2017.2771560
[13]	X. D. Li, D. X. Peng, J. D. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE T. Automat. Contr., 65 (2020), 4908–4913. https://doi.org/10.1109/TAC.2020.2964558 doi: 10.1109/TAC.2020.2964558
[14]	R. Kumar, U. Kumar, S. Das, J. L. Qiu, J. Q. Lu, Effects of heterogeneous impulses on synchronization of complex-valued neural networks with mixed time-varying delays, Inform. Sci., 551 (2021), 228–244. https://doi.org/10.1016/j.ins.2020.10.064 doi: 10.1016/j.ins.2020.10.064
[15]	W. L. He, F. Qian, J. Lam, G. R. Chen, Q. L. Han, J. Kurths, Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: Error estimation, optimization and design, Automatica, 62 (2015), 249–262. https://doi.org/10.1016/j.automatica.2015.09.028 doi: 10.1016/j.automatica.2015.09.028
[16]	Y. F. Zhou, H. Zhang, Z. G. Zeng, Quasi-synchronization of delayed memristive neural networks via a hybrid impulsive control, IEEE T. Syst. Man Cy. -S, 51 (2021), 1954–1965. https://doi.org/10.1109/TSMC.2019.2911366 doi: 10.1109/TSMC.2019.2911366
[17]	W. L. He, G. R. Chen, Q. L. Han, F. Qian, Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control, Inform. Sci., 380 (2017), 145–158. https://doi.org/10.1016/j.ins.2015.06.005 doi: 10.1016/j.ins.2015.06.005
[18]	Y. W. Wang, W. Yang, J. W. Xiao, Z. G. Zeng, Impulsive multisynchronization of coupled multistable neural networks with time-varying delay, IEEE T. Neur. Net. Lear., 28 (2017), 1560–1571. https://doi.org/10.1109/TNNLS.2016.2544788 doi: 10.1109/TNNLS.2016.2544788
[19]	X. W. Liu, T. P. Chen, Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control, IEEE T. Neur. Net. Lear., 26 (2015), 113–126. https://doi.org/10.1109/TNNLS.2014.2311838 doi: 10.1109/TNNLS.2014.2311838
[20]	C. B. Yi, J. W. Feng, J. Y. Wang, C. X Xu, Y. Zhao, Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control, Appl. Math. Comput., 312 (2017), 78–90. https://doi.org/10.1016/j.amc.2017.04.030 doi: 10.1016/j.amc.2017.04.030
[21]	Y. F. Shen, J. Y. Shi, S. M. Cai, Exponential synchronization of directed bipartite networks with node delays and hybrid coupling via impulsive pinning control, Neurocomputing, 453 (2021), 209–222. https://doi.org/10.1016/j.neucom.2021.04.097 doi: 10.1016/j.neucom.2021.04.097
[22]	G. Ling, X. Z. Liu, M. F. Ge, Y. H. Wu, Delay-dependent cluster synchronization of time-varying complex dynamical networks with noise via delayed pinning impulsive control, J. Franklin Inst., 358 (2021), 3193–3214. https://doi.org/10.1016/j.jfranklin.2021.02.004 doi: 10.1016/j.jfranklin.2021.02.004
[23]	Q. H. Fu, S. M. Zhong, K. B. Shi, Exponential synchronization of memristive neural networks with inertial and nonlinear coupling terms: Pinning impulsive control approaches, Appl. Math. Comput., 402 (2021), 126169. https://doi.org/10.1016/j.amc.2021.126169 doi: 10.1016/j.amc.2021.126169
[24]	T. Wu, L. L. Xiong, J. D. Cao, J. H. Park, J. Cheng, Synchronization of coupled reaction-diffusion stochastic neural networks with time-varying delay via delay-dependent impulsive pinning control algorithm, Commun. Nonlinear Sci. Numer. Simul., 99 (2021), 105777. https://doi.org/10.1016/j.cnsns.2021.105777 doi: 10.1016/j.cnsns.2021.105777
[25]	A. Borri, P. Pepe, Event-triggered control of nonlinear systems with time-varying state delays, IEEE T. Automat. Contr., 66, (2021), 2846–2853. https://doi.org/10.1109/TAC.2020.3009173 doi: 10.1109/TAC.2020.3009173
[26]	K. Hashimoto, S. Adachi, D. V. Dimarogonas, Event-triggered intermittent sampling for nonlinear model predictive control, Automatica, 81 (2017), 148–155. https://doi.org/10.1016/j.automatica.2017.03.028 doi: 10.1016/j.automatica.2017.03.028
[27]	G. L. Zhao, C. C. Hua, X. P. Guan, Distributed event-triggered consensus of multiagent systems with communication delays: A hybrid system approach, IEEE T. Cybernetics, 50 (2020), 3169–3181. https://doi.org/10.1109/TCYB.2019.2912403 doi: 10.1109/TCYB.2019.2912403
[28]	J. Liu, Y. Zhang, Y. Yu, C. Sun, Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications, IEEE T. Syst. Man Cy. B, 49 (2019), 2221–2229.
[29]	Y. W. Wang, Y. Lei, T. Bian, Z. H. Guan, Distributed control of nonlinear multiagent systems with unknown and nonidentical control directions via event-triggered communication, IEEE T. Cybernetics, 50 (2020), 1820–1832. https://doi.org/10.1109/TCYB.2019.2908874 doi: 10.1109/TCYB.2019.2908874
[30]	W. Zhu, D. D. Wang, L. Liu, G. Feng, Event-based impulsive control of continuous-time dynamic systems and its application to synchronization of memristive neural networks, IEEE T. Neur. Net. Lear., 29 (2018), 3599–3609. https://doi.org/10.1109/TNNLS.2017.2731865 doi: 10.1109/TNNLS.2017.2731865
[31]	D. X. Peng, X. D. Li, Leader-following synchronization of complex dynamic networks via event-triggered impulsive control, Neurocomputing, 412 (2020), 1–10. https://doi.org/10.1016/j.neucom.2020.05.071 doi: 10.1016/j.neucom.2020.05.071
[32]	B. Liu, Z. J. Sun, Y. H. Luo, Y. X. Zhong, Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control, Phys. A, 531 (2019), 121725. https://doi.org/10.1016/j.physa.2019.121725 doi: 10.1016/j.physa.2019.121725
[33]	W. O. Kermack, A. G. McKendrick, Contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 115 (1927), 700–721. https://doi.10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
[34]	P. Yang, J. B. Jia, W. Shi, J. W. Feng, X. C. Fu, Stability analysis and optimal control in an epidemic model on directed complex networks with nonlinear incidence, Commun. Nonlinear Sci. Numer. Simul., 121 (2023), 107206. https://doi.org/10.1016/j.cnsns.2023.107206 doi: 10.1016/j.cnsns.2023.107206
[35]	K. M. Bi, Y. Y. Chen, C. H. Wu, D. Ben-Arieh, Learning-based impulse control with event-triggered conditions for an epidemic dynamic system, Commun. Nonlinear Sci. Numer. Simul., 108 (2022), 106204–106204. https://doi.org/10.1016/j.cnsns.2021.106204 doi: 10.1016/j.cnsns.2021.106204
[36]	X. X. Lv, J. D. Cao, X. D. Li, M. Abdel-Aty, U. A. Al-Juboori, Synchronization analysis for complex dynamical networks with coupling delay via event-triggered delayed impulsive control, IEEE T. Cybernetics, 51 (2021), 5269–5278. https://doi.org/10.1109/TCYB.2020.2974315 doi: 10.1109/TCYB.2020.2974315
[37]	Y. F. Zhou, Z. G. Zeng, Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays, Neural Networks, 110 (2019), 55–65. https://doi.org/10.1016/j.neunet.2018.09.014 doi: 10.1016/j.neunet.2018.09.014
[38]	X. D. Li, J. H. Wu, Stability of nonlinear differential systems with state-dependent delayed impulses, Automatica, 64 (2016), 63–69. https://doi.org/10.1016/j.automatica.2015.10.002 doi: 10.1016/j.automatica.2015.10.002
[39]	X. D. Li, X. Y. Yang, J. D. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica, 117 (2020), 108981. https://doi.org/10.1016/j.automatica.2020.108981 doi: 10.1016/j.automatica.2020.108981
[40]	D. Liu, D. Ye, Exponential synchronization of memristive delayed neural networks via event-based impulsive control method, J. Franklin Inst., 357 (2020), 4437–4457. https://doi.org/10.1016/j.jfranklin.2020.03.011 doi: 10.1016/j.jfranklin.2020.03.011
[41]	W. H. Chen, W. X. Zheng, X. M. Lu, Impulsive stabilization of a class of singular systems with time-delays, Automatica, 83 (2017), 28–36. https://doi.org/10.1016/j.automatica.2017.05.008 doi: 10.1016/j.automatica.2017.05.008
[42]	G. Ling, M. F. Ge, X. H. Liu, G. X. Xiao, Q. J. Fan, Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control, Neural Networks, 139 (2021), 223–236. https://doi.org/10.1016/j.neunet.2021.03.011 doi: 10.1016/j.neunet.2021.03.011
[43]	G. H. Mu, L. L. Li, X. D. Li, Quasi-bipartite synchronization of signed delayed neural networks under impulsive effects, Neural Networks, 129 (2020), 31–42. https://doi.org/10.1016/j.neunet.2020.05.012 doi: 10.1016/j.neunet.2020.05.012
[44]	Z. L. Xu, X. D. Li, P. Y. Duan, Synchronization of complex networks with time-varying delay of unknown bound via delayed impulsive control, Neural Networks, 125 (2020), 224–232. https://doi.org/10.1016/j.neunet.2020.02.003 doi: 10.1016/j.neunet.2020.02.003
[45]	Y. Q. Wang, J. Q. Lu, X. D. Li, J. L. Liang, Synchronization of coupled neural networks under mixed impulsive effects: A novel delay inequality approach, Neural Networks, 127 (2020), 38–46. https://doi.org/10.1016/j.neunet.2020.04.002 doi: 10.1016/j.neunet.2020.04.002
[46]	S. Boyd, E. I. Ghaoui, E. Feron, V. Balakrishnana, Linear matrix inequalities in system and control theory, 1994. https://doi.org/10.1137/1.9781611970777
[47]	W. L. Lu, T. P. Chen, New approach to synchronization analysis of linearly coupled ordinary differential systems, Phys. D, 213 (2006), 214–230. https://doi.org/10.1016/j.physd.2005.11.009 doi: 10.1016/j.physd.2005.11.009

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)