Exponential synchronization analysis for complex dynamical networks with hybrid delays and uncertainties under given control parameters

Saravanan Shanmugam; Mohamed Rhaima; Hamza Ghoudi; Saravanan Shanmugam; Mohamed Rhaima; Hamza Ghoudi

doi:10.3934/math.20231484

AIMS Mathematics

2023, Volume 8, Issue 12: 28976-29007. doi: 10.3934/math.20231484

Previous Article Next Article

Research article

Exponential synchronization analysis for complex dynamical networks with hybrid delays and uncertainties under given control parameters

1.
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600 069, Tamil Nadu, India
2.
Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455 Riyadh 11451, Saudi Arabia
3.
University of Paris Nanterre, MODAL'X, BAT G, 200, ave de la République 92000 Nanterre, France

Received: 29 August 2023 Revised: 03 October 2023 Accepted: 11 October 2023 Published: 25 October 2023
MSC : 93B20, 92D20

This paper addresses the problem of exponential synchronization in continuous-time complex dynamical networks with both time-delayed and non-delayed interactions. We employ a proportional integral derivative (PID) control strategy and a dynamic event-triggered approach to investigate this synchronization problem. Our approach begins with constructing a general model for complex dynamical networks that incorporate delays. We then derive synchronization criteria based on the PID control parameters, utilizing linear matrix inequality techniques in conjunction with a dynamic event-trigger mechanism. The application of Lyapunov stability theory and inequality techniques allows us to establish these criteria, considering the presence of hybrid delays. To illustrate the effectiveness of our proposed model, we provide two numerical examples showcasing synchronization dynamics. These examples demonstrate the successful theoretical results of a novel PID controller and dynamic event-trigger mechanism.
- complex dynamical networks,
- exponential synchronization,
- Lyapunov-Krasovskii functional,
- PID control
Citation: Saravanan Shanmugam, Mohamed Rhaima, Hamza Ghoudi. Exponential synchronization analysis for complex dynamical networks with hybrid delays and uncertainties under given control parameters[J]. AIMS Mathematics, 2023, 8(12): 28976-29007. doi: 10.3934/math.20231484

Related Papers:

Abstract

This paper addresses the problem of exponential synchronization in continuous-time complex dynamical networks with both time-delayed and non-delayed interactions. We employ a proportional integral derivative (PID) control strategy and a dynamic event-triggered approach to investigate this synchronization problem. Our approach begins with constructing a general model for complex dynamical networks that incorporate delays. We then derive synchronization criteria based on the PID control parameters, utilizing linear matrix inequality techniques in conjunction with a dynamic event-trigger mechanism. The application of Lyapunov stability theory and inequality techniques allows us to establish these criteria, considering the presence of hybrid delays. To illustrate the effectiveness of our proposed model, we provide two numerical examples showcasing synchronization dynamics. These examples demonstrate the successful theoretical results of a novel PID controller and dynamic event-trigger mechanism.

References

[1]	Y. Yu, Z. Zhang, M. Zhong, Z. Wang, Pinning synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval, J. Franklin I., 359 (2022), 1434–1456. https://doi.org/10.1016/j.jfranklin.2021.11.036 doi: 10.1016/j.jfranklin.2021.11.036
[2]	H. Zhao, L. Li, H. Peng, J. Xiao, Y. Yang, M. Zheng, Impulsive control for synchronization and parameters identification of uncertain multi-links complex network, Nonlinear Dyn., 83 (2016), 1437–1451. https://doi.org/10.1007/S11071-015-2416-3 doi: 10.1007/S11071-015-2416-3
[3]	W. Yu, G. Chen, J. Lü, On pinning synchronization of complex dynamical networks, Automatica, 45 (2009), 429–435. https://doi.org/10.1016/j.automatica.2008.07.016 doi: 10.1016/j.automatica.2008.07.016
[4]	H. Liu, J. A. Lu, J. Lü, D. J. Hill, Structure identification of uncertain general complex dynamical networks with time delay, Automatica, 45 (2009), 1799–1807. https://doi.org/10.1016/j.automatica.2009.03.022 doi: 10.1016/j.automatica.2009.03.022
[5]	H. Ren, F. Deng, Y. Peng, Finite time synchronization of markovian jumping stochastic complex dynamical systems with mix delays via hybrid control strategy, Neurocomputing, 272 (2018), 683–693. https://doi.org/10.1016/j.neucom.2017.08.013 doi: 10.1016/j.neucom.2017.08.013
[6]	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 T. Circuits-I, 57 (2010), 2182–2195. https://doi.org/10.1109/TCSI.2009.2037848 doi: 10.1109/TCSI.2009.2037848
[7]	L. Xiao, B. Liao, S. Li, Z. Zhang, L. Ding, L. Jin, Design and analysis of ftznn applied to the real-time solution of a nonstationary lyapunov equation and tracking control of a wheeled mobile manipulator, IEEE T. Ind. Inform., 14 (2018), 98–105. https://doi.org/10.1109/TII.2017.2717020 doi: 10.1109/TII.2017.2717020
[8]	L. Xiao, J. Dai, L. Jin, W. Li, S. Li, J. Hou, A noise-enduring and finite-time zeroing neural network for equality-constrained time-varying nonlinear optimization, IEEE T. Syst. Man Cy.-S., 51 (2021), 4729–4740. https://doi.org/10.1109/TSMC.2019.2944152 doi: 10.1109/TSMC.2019.2944152
[9]	J. Zhou, D. Xu, W. Tai, C. K. Ahn, Switched event-triggered $H_\infty$ security control for networked systems vulnerable to aperiodic dos attacks, IEEE T. Netw. Sci. Eng., 10 (2023), 2109–2123. https://doi.org/10.1109/TNSE.2023.3243095 doi: 10.1109/TNSE.2023.3243095
[10]	J. L. Wang, P. C. Wei, H. N. Wu, T. Huang, M. Xu, Pinning synchronization of complex dynamical networks with multiweights, IEEE T. Syst. Man Cy.-S., 49 (2019), 1357–1370. https://doi.org/10.1109/TSMC.2017.2754466 doi: 10.1109/TSMC.2017.2754466
[11]	Q. Li, B. Shen, Z. Wang, T. Huang, J. Luo, Synchronization control for a class of discrete time-delay complex dynamical networks: A dynamic event-triggered approach, IEEE T. Cybernetics, 49 (2019), 1979–1986. https://doi.org/10.1109/TCYB.2018.2818941 doi: 10.1109/TCYB.2018.2818941
[12]	X. Yang, J. Lam, D. W. C. Ho, Z. Feng, Fixed-time synchronization of complex networks with impulsive effects via nonchattering control, IEEE T. Automat. Contr., 62 (2017), 5511–5521. https://doi.org/10.1109/TAC.2017.2691303 doi: 10.1109/TAC.2017.2691303
[13]	H. Shen, X. Hu, X. Wu, S. He, J. Wang, Generalized dissipative state estimation of singularly perturbed switched complex dynamic networks with persistent dwell-time mechanism, IEEE T. Syst. Man Cy.-S., 52 (2020), 1795–1806. https://doi.org/10.1109/TSMC.2020.3034635 doi: 10.1109/TSMC.2020.3034635
[14]	M. S. Raunak, L. J. Osterweil, Resource management for complex, dynamic environments, IEEE T. Software Eng., 39 (2012), 384–402. https://doi.org/10.1109/TSE.2012.31 doi: 10.1109/TSE.2012.31
[15]	L. Wang, H. P. Dai, H. Dong, Y. Y. Cao, Y. X. Sun, Adaptive synchronization of weighted complex dynamical networks through pinning, Eur. Phys. J. B, 61 (2008), 335–342. https://doi.org/10.1140/epjb/e2008-00081-5 doi: 10.1140/epjb/e2008-00081-5
[16]	J. Yogambigai, M. S. Ali, H. Alsulami, M. S. Alhodaly, Impulsive and pinning control synchronization of markovian jumping complex dynamical networks with hybrid coupling and additive interval time-varying delays, Commun. Nonlinear Sci., 85 (2020), 105215. https://doi.org/10.1016/j.cnsns.2020.105215 doi: 10.1016/j.cnsns.2020.105215
[17]	M. S. Anwar, S. Kundu, D. Ghosh, Enhancing synchrony in asymmetrically weighted multiplex networks, Chaos Soliton. Fract., 142 (2021), 110476. https://doi.org/10.1016/j.chaos.2020.110476 doi: 10.1016/j.chaos.2020.110476
[18]	M. S. Anwar, D. Ghosh, N. Frolov, Relay synchronization in a weighted triplex network, Mathematics, 9 (2021), 2135. https://doi.org/10.3390/math9172135 doi: 10.3390/math9172135
[19]	L. V. Gambuzza, M. Frasca, E. Estrada, Hubs-attracting laplacian and related synchronization on networks, SIAM J. Appl. Dyn. Syst., 19 (2020), 1057–1079. https://doi.org/10.1137/19M1287663 doi: 10.1137/19M1287663
[20]	Y. A. Liu, J. Xia, B. Meng, X. Song, H. Shen, Extended dissipative synchronization for semi-markov jump complex dynamic networks via memory sampled-data control scheme, J. Franklin I., 357 (2020), 10900–10920. https://doi.org/10.1016/j.jfranklin.2020.08.023 doi: 10.1016/j.jfranklin.2020.08.023
[21]	Y. Wang, S. Ding, R. Li, Master-slave synchronization of neural networks via event-triggered dynamic controller, Neurocomputing, 419 (2021), 215–223. https://doi.org/10.1016/j.neucom.2020.08.062 doi: 10.1016/j.neucom.2020.08.062
[22]	Q. Jia, E. S. Mwanandiye, W. K. Tang, Master-slave synchronization of delayed neural networks with time-varying control, IEEE T. Neur. Net. Lear., 32 (2021), 2292–2298. https://doi.org/10.1109/TNNLS.2020.2996224 doi: 10.1109/TNNLS.2020.2996224
[23]	C. Hu, H. He, H. Jiang, Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability, IEEE T. Cybernetics, 51 (2021), 2882–2892. https://doi.org/10.1109/TCYB.2020.2977934 doi: 10.1109/TCYB.2020.2977934
[24]	J. Zhang, J. Sun, Exponential synchronization of complex networks with continuous dynamics and boolean mechanism, Neurocomputing, 307 (2018), 146–152. https://doi.org/10.1016/j.neucom.2018.03.061 doi: 10.1016/j.neucom.2018.03.061
[25]	A. Z. Dragicevic, A. Gurtoo, Stochastic control of ecological networks, J. Math. Biol., 85 (2022), 7. https://doi.org/10.1007/s00285-022-01777-5 doi: 10.1007/s00285-022-01777-5
[26]	J. L. Wang, H. N. Wu, T. Huang, S. Y. Ren, Analysis and pinning control for output synchronization and $h_{\infty}$ output synchronization of multi-weighted complex networks, In: Analysis and control of output synchronization for complex dynamical networks, Singapore: Springer, 2019,175–205. https://doi.org/10.1007/978-981-13-1352-3_9
[27]	D. Wang, W. W. Che, H. Yu, J. Y. Li, Adaptive pinning synchronization of complex networks with negative weights and its application in traffic road network, Int. J. Control Autom. Syst., 16 (2018), 782–790. https://doi.org/10.1007/s12555-017-0161-8 doi: 10.1007/s12555-017-0161-8
[28]	E. Kyriakakis, J. Sparsø, P. Puschner, M. Schoeberl, Synchronizing real-time tasks in time-triggered networks, In: 2021 IEEE 24th international symposium on real-time distributed computing (ISORC), 2021, 11–19. https://doi.org/10.1109/ISORC52013.2021.00013
[29]	T. Hu, Z. He, X. Zhang, S. Zhong, K. Shi, Y. Zhang, Adaptive fuzzy control for quasi-synchronization of uncertain complex dynamical networks with time-varying topology via event-triggered communication strategy, Inform. Sci., 582 (2022), 704–724. https://doi.org/10.1016/j.ins.2021.10.036 doi: 10.1016/j.ins.2021.10.036
[30]	K. Krüger, G. Fohler, M. Völp, P. Esteves-Verissimo, Improving security for time-triggered real-time systems with task replication, In: 2018 IEEE 24th international conference on embedded and real-time computing systems and applications (RTCSA), 2018,232–233. https://doi.org/10.1109/RTCSA.2018.00036
[31]	Q. Wang, B. Fu, C. Lin, P. Li, Exponential synchronization of chaotic lur'e systems with time-triggered intermittent control, Commun. Nonlinear Sci., 109 (2022), 106298. https://doi.org/10.1016/j.cnsns.2022.106298 doi: 10.1016/j.cnsns.2022.106298
[32]	S. Ding, Z. Wang, Event-triggered synchronization of discrete-time neural networks: A switching approach, Neural Networks, 125 (2020), 31–40. https://doi.org/10.1016/j.neunet.2020.01.024 doi: 10.1016/j.neunet.2020.01.024
[33]	Y. Li, F. Song, J. Liu, X. Xie, E. Tian, Decentralized event-triggered synchronization control for complex networks with nonperiodic dos attacks, Int. J. Robust Nonlin., 32 (2022), 1633–1653. https://doi.org/10.1002/rnc.5899 doi: 10.1002/rnc.5899
[34]	R. Pan, Y. Tan, D. Du, S. Fei, Adaptive event-triggered synchronization control for complex networks with quantization and cyber-attacks, Neurocomputing, 382 (2020), 249–258. https://doi.org/10.1016/j.neucom.2019.11.096 doi: 10.1016/j.neucom.2019.11.096
[35]	W. Xing, P. Shi, R. K. Agarwal, L. Li, Robust ${H}_\infty$ pinning synchronization for complex networks with event-triggered communication scheme, IEEE T. Circuits Syst.-I, 67 (2020), 5233–5245. https://doi.org/10.1109/TCSI.2020.3004170 doi: 10.1109/TCSI.2020.3004170
[36]	B. Li, Z. Wang, L. Ma, An event-triggered pinning control approach to synchronization of discrete-time stochastic complex dynamical networks, IEEE T. Neur. Net. Lear., 29 (2018), 5812–5822. https://doi.org/10.1109/TNNLS.2018.2812098 doi: 10.1109/TNNLS.2018.2812098
[37]	Y. Luo, Y. Yao, Z. Cheng, X. Xiao, H. Liu, Event-triggered control for coupled reaction–diffusion complex network systems with finite-time synchronization, Physica A, 562 (2021), 125219. https://doi.org/10.1016/j.physa.2020.125219 doi: 10.1016/j.physa.2020.125219
[38]	X. Lv, J. Cao, X. 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
[39]	C. X. Shi, G. H. Yang, X. J. Li, Event-triggered output feedback synchronization control of complex dynamical networks, Neurocomputing, 275 (2018), 29–39. https://doi.org/10.1016/j.neucom.2017.05.014 doi: 10.1016/j.neucom.2017.05.014
[40]	X. Li, H. Wu, J. Cao, A new prescribed-time stability theorem for impulsive piecewise-smooth systems and its application to synchronization in networks, Appl. Math. Model., 115 (2023), 385–397. https://doi.org/10.1016/j.apm.2022.10.051 doi: 10.1016/j.apm.2022.10.051
[41]	X. Li, H. Wu, J. Cao, Prescribed-time synchronization in networks of piecewise smooth systems via a nonlinear dynamic event-triggered control strategy, Math. Comput. Simulat., 203 (2023), 647–668. https://doi.org/10.1016/j.matcom.2022.07.010 doi: 10.1016/j.matcom.2022.07.010
[42]	B. Zhou, X. Liao, T. Huang, G. Chen, Pinning exponential synchronization of complex networks via event-triggered communication with combinational measurements, Neurocomputing, 157 (2015), 199–207. https://doi.org/10.1016/j.neucom.2015.01.018 doi: 10.1016/j.neucom.2015.01.018
[43]	D. Liu, G. H. Yang, Event-triggered synchronization control for complex networks with actuator saturation, Neurocomputing, 275 (2018), 2209–2216. https://doi.org/10.1016/j.neucom.2017.10.054 doi: 10.1016/j.neucom.2017.10.054
[44]	J. Liu, H. Wu, J. Cao, Event-triggered synchronization in fixed time for semi-markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity, Commun. Nonlinear Sci., 90 (2020), 105400. https://doi.org/10.1016/j.cnsns.2020.105400 doi: 10.1016/j.cnsns.2020.105400
[45]	X. Song, R. Zhang, C. K. Ahn, S. Song, Dissipative synchronization of semi-markov jump complex dynamical networks via adaptive event-triggered sampling control scheme, IEEE Syst. J., 16 (2022), 4653–4663. https://doi.org/10.1109/JSYST.2021.3124082 doi: 10.1109/JSYST.2021.3124082
[46]	Q. Dong, P. Yu, Y. Ma, Event-triggered synchronization control of complex networks with adaptive coupling strength, J. Franklin I., 359 (2022), 1215–1234. https://doi.org/10.1016/j.jfranklin.2021.11.007 doi: 10.1016/j.jfranklin.2021.11.007
[47]	H. Lu, Y. Hu, C. Guo, W. Zhou, Cluster synchronization for a class of complex dynamical network system with randomly occurring coupling delays via an improved event-triggered pinning control approach, J. Franklin I., 357 (2020), 2167–2184. https://doi.org/10.1016/j.jfranklin.2019.11.076 doi: 10.1016/j.jfranklin.2019.11.076
[48]	S. Wang, Y. Cao, T. Huang, Y. Chen, S. Wen, Event-triggered distributed control for synchronization of multiple memristive neural networks under cyber-physical attacks, Inform. Sci., 518 (2020), 361–375. https://doi.org/10.1016/j.ins.2020.01.022 doi: 10.1016/j.ins.2020.01.022
[49]	W. Wu, L. He, J. Zhou, Z. Xuan, S. Arik, Disturbance-term-based switching event-triggered synchronization control of chaotic lurie systems subject to a joint performance guarantee, Commun. Nonlinear Sci., 115 (2022), 106774. https://doi.org/10.1016/j.cnsns.2022.106774 doi: 10.1016/j.cnsns.2022.106774
[50]	Y. Ni, Z. Wang, Y. Fan, X. Huang, H. Shen, Memory-based event-triggered control for global synchronization of chaotic lur'e systems and its application, IEEE T. Syst. Man Cy.-S., 53 (2023), 1920–1931. https://doi.org/10.1109/TSMC.2022.3207353 doi: 10.1109/TSMC.2022.3207353
[51]	H. Zhang, J. Liu, Event-triggered fuzzy flight control of a two-degree-of-freedom helicopter system, IEEE T. Fuzzy Syst., 29 (2021), 2949–2962. https://doi.org/10.1109/TFUZZ.2020.3009755 doi: 10.1109/TFUZZ.2020.3009755
[52]	P. Liu, H. Gu, Y. Kang, J. Lü, Global synchronization under {PI/PD} controllers in general complex networks with time-delay, Neurocomputing, 366 (2019), 12–22. https://doi.org/10.1016/j.neucom.2019.07.028 doi: 10.1016/j.neucom.2019.07.028
[53]	H. Gu, P. Liu, J. Lü, Z. Lin, PID control for synchronization of complex dynamical networks with directed topologies, IEEE T. Cybernetics, 51 (2021), 1334–1346. https://doi.org/10.1109/tcyb.2019.2902810 doi: 10.1109/tcyb.2019.2902810
[54]	S. Aadhithiyan, R. Raja, Q. Zhu, J. Alzabut, M. Niezabitowski, C. P. Lim, Exponential synchronization of nonlinear multi-weighted complex dynamic networks with hybrid time varying delays, Neural Process. Lett., 53 (2021), 1035–1063. https://doi.org/10.1007/s11063-021-10428-7 doi: 10.1007/s11063-021-10428-7
[55]	J. Suo, M. Shi, Y. Li, Y. Yang, Proportional-integral control for synchronization of complex dynamical networks under dynamic event-triggered mechanism, J. Franklin I., 360 (2023), 1436–1453. https://doi.org/10.1016/j.jfranklin.2022.09.048 doi: 10.1016/j.jfranklin.2022.09.048
[56]	S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM, 1994.
[57]	H. Liu, T. Wang, Exponential synchronization of complex dynamical networks via a novel sampled-data control, Complexity, 2022 (2022), 2786011. https://doi.org/10.1155/2022/2786011 doi: 10.1155/2022/2786011
[58]	Y. He, M. Wu, J. H. She, Delay-dependent exponential stability of delayed neural networks with time-varying delay, IEEE T. Circuits-Ⅱ, 53 (2006), 553–557. https://doi.org/10.1109/TCSII.2006.876385 doi: 10.1109/TCSII.2006.876385

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)