Event-triggered fixed/preassigned time stabilization of state-dependent switching neural networks with mixed time delays

Jiashu Gao; Jing Han; Guodong Zhang; Jiashu Gao; Jing Han; Guodong Zhang

doi:10.3934/math.2024449

AIMS Mathematics

2024, Volume 9, Issue 4: 9211-9231. doi: 10.3934/math.2024449

Previous Article Next Article

Research article Special Issues

Event-triggered fixed/preassigned time stabilization of state-dependent switching neural networks with mixed time delays

1.
College of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
2.
School of Information Engineering, Wuhan Business University, Wuhan 430056, China

Received: 14 January 2024 Revised: 23 February 2024 Accepted: 28 February 2024 Published: 06 March 2024
MSC : 34H15, 34K34

This study employed an event-triggered control (ETC) strategy to investigate the problems of fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) for state-dependent switching neural networks (SDSNNs) that involved mixed time delays. To enhance the network's generalization capability and accelerate convergence stabilization, a more intricate weight-switching mechanism was introduced, then to mitigate transmission energy consumption, this paper proposed a tailored event-triggering rule that triggered the ETC solely at predetermined time points. This rule ensured the stability of the system while effectively reducing energy consumption. Using the Lyapunov stability theory and various inequality techniques, this paper presented new results for FTS and PTS of SDSNNs. The validity of these findings was supported by conducting data simulations in two illustrative examples.
- fixed/preassigned-time stabilization,
- event-triggered control,
- state-dependent switching,
- mixed time delays
Citation: Jiashu Gao, Jing Han, Guodong Zhang. Event-triggered fixed/preassigned time stabilization of state-dependent switching neural networks with mixed time delays[J]. AIMS Mathematics, 2024, 9(4): 9211-9231. doi: 10.3934/math.2024449

Related Papers:

Abstract

This study employed an event-triggered control (ETC) strategy to investigate the problems of fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) for state-dependent switching neural networks (SDSNNs) that involved mixed time delays. To enhance the network's generalization capability and accelerate convergence stabilization, a more intricate weight-switching mechanism was introduced, then to mitigate transmission energy consumption, this paper proposed a tailored event-triggering rule that triggered the ETC solely at predetermined time points. This rule ensured the stability of the system while effectively reducing energy consumption. Using the Lyapunov stability theory and various inequality techniques, this paper presented new results for FTS and PTS of SDSNNs. The validity of these findings was supported by conducting data simulations in two illustrative examples.

References

[1]	J. Cheng, X. Jiang, H. Zhou, J. Dong, Research progress and challenges of photoelectric intelligent computing, China Laser, 49 (2022), 327–339.
[2]	L. Chua, Memristor-the missing circuit element, IEEE Trans. Circuit Theory, 18 (1971), 507–519. https://doi.org/10.1109/TCT.1971.1083337 doi: 10.1109/TCT.1971.1083337
[3]	D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, The missing memristor found, Nature, 453 (2008), 80–83.
[4]	G. Zhang, Z. Zeng, D. Ning, Novel results on synchronization for a class of switched inertial neural networks with distributed delays, Inf. Sci., 511 (2020), 114–126. https://doi.org/10.1016/j.ins.2019.09.048 doi: 10.1016/j.ins.2019.09.048
[5]	G. Zhang, J. Cao, A. Kashkynbayev, Further results on fixed/preassigned-time projective lag synchronization control of hybrid inertial neural networks with time delays, J. Franklin Inst., 360 (2023), 9950–9973. https://doi.org/10.1016/j.jfranklin.2023.07.040 doi: 10.1016/j.jfranklin.2023.07.040
[6]	G. Milano, M. Agliuzza, N. de Leo, C. Ricciardi, Speech recognition through physical reservoir computing with neuromorphic nanowire networks, 2022 International Joint Conference on Neural Networks (IJCNN), 2022. https://doi.org/10.1109/IJCNN55064.2022.9892078
[7]	J. X. Zhang, T. Yang, T. Chai, Neural network control of underactuated surface vehicles with prescribed trajectory tracking performance, IEEE Trans. Neural Networks Learn. Syst., 2022. https://doi.org/10.1109/TNNLS.2022.3223666
[8]	G. Qin, A. Lin, J. Cheng, M. Hu, I. Katib, Protocol-based fault detection filtering for memristive neural networks with dynamic quantization, J. Franklin Inst., 360 (2023), 13395–13413. https://doi.org/10.1016/j.jfranklin.2023.10.019 doi: 10.1016/j.jfranklin.2023.10.019
[9]	J. X. Zhang, T. Chai, Proportional-integral funnel control of unknown lower-triangular nonlinear systems, IEEE Trans. Autom. Control, 2023. https://doi.org/10.1109/TAC.2023.3330900
[10]	C. Xu, W. Ou, Y. Pang, Q. Cui, M. U. Rahman, M. Farman, et al., Hopf bifurcation control of a fractional-order delayed turbidostat model via a novel extended hybrid controller, MATCH Commun. Math. Comput. Chem., 91 (2024), 367–413. https://doi.org/10.46793/match.91-2.367X doi: 10.46793/match.91-2.367X
[11]	C. Xu, Z. Liu, P. Li, J. Yan, L. Yao, Bifurcation mechanism for fractional-order three-triangle multi-delayed neural networks, Neural Process. Lett., 55 (2023), 6125–6151. https://doi.org/10.1007/s11063-022-11130-y doi: 10.1007/s11063-022-11130-y
[12]	C. Xu, Q. Cui, Z. Liu, Y. Pan, X. Cui, W. Ou, et al., Extended hybrid controller design of bifurcation in a delayed chemostat model, MATCH Commun. Math. Comput. Chem., 90 (2023), 609–648. https://doi.org/10.46793/match.90-3.609X doi: 10.46793/match.90-3.609X
[13]	H. Guo, J. Han, G. Zhang, Hopf bifurcation and control for the bioeconomic predator-prey model with square root functional response and nonlinear prey harvesting, Mathematics, 11 (2023), 4958. https://doi.org/10.3390/math11244958 doi: 10.3390/math11244958
[14]	M. J. Mirzaei, E. Aslmostafa, M. Asadollahi, M. A. Badamchizadeh, Robust adaptive finite-time stabilization control for a class of nonlinear switched systems based on finite-time disturbance observer, J. Franklin Inst., 358 (2021), 3332–3352. https://doi.org/10.1016/j.jfranklin.2021.02.010 doi: 10.1016/j.jfranklin.2021.02.010
[15]	N. Xu, Y. Chen, A. Xue, G. Zong, Finite-time stabilization of continuous-time switched positive delayed systems, J. Franklin Inst., 359 (2022), 255–271. https://doi.org/10.1016/j.jfranklin.2021.04.022 doi: 10.1016/j.jfranklin.2021.04.022
[16]	S. Kanakalakshmi, R. Sakthivel, S. Karthick, A. Leelamani, A. Parivallal, Finite-time decentralized event-triggering non-fragile control for fuzzy neural networks with cyber-attack and energy constraints, Eur. J. Control, 57 (2021), 135–146, https://doi.org/10.1016/j.ejcon.2020.05.001 doi: 10.1016/j.ejcon.2020.05.001
[17]	M. M. Silva, X. Wang, F. E. Alsaadi, Y. Shen, Fixed-time synchronization and parameter identification of coupled neural networks, Neural Networks, 77 (2016), 40–47.
[18]	X. Hu, L. Wang, C. K. Zhang, X. Wan, Y. He, Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control, Sci. China Inf. Sci., 66 (2023), 152204. https://doi.org/10.1007/s11432-022-3633-9 doi: 10.1007/s11432-022-3633-9
[19]	Y. Bao, Y. Zhang, B. Zhang, Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks, Neural Networks, 163 (2023), 312–326, https://doi.org/10.1016/j.neunet.2023.04.003 doi: 10.1016/j.neunet.2023.04.003
[20]	G. Zhang, Novel results on event-triggered-based fixed-time synchronization and stabilization of discontinuous neural networks with distributed delays, Franklin Open, 4 (2023), 100032. https://doi.org/10.1016/j.fraope.2023.100032 doi: 10.1016/j.fraope.2023.100032
[21]	Y. Zhang, F. Kong, L. Wang, C. Hu, Fixed-time stabilization of generalized leakage-delayed neural networks with discontinuous disturbances via mixed-delay-product-type LKF, Eur. J. Control, 71 (2023), 100793. https://doi.org/10.1016/j.ejcon.2023.100793 doi: 10.1016/j.ejcon.2023.100793
[22]	F. Tan, L. Zhou, J. Lu, H. Zhang, Fixed-time synchronization in multilayer networks with delay cohen–grossberg neural subnets via adaptive quantitative control, Asian J. Control, 26 (2024), 446–455. https://doi.org/10.1002/asjc.3217 doi: 10.1002/asjc.3217
[23]	Q. Gan, L. Li, J. Yang, Y. Qin, M. Meng, Improved results on fixed-/preassigned-time synchronization for memristive complex-valued neural networks, IEEE Trans. Neural Networks Learn. Syst., 33 (2021), 5542–5556. https://doi.org/10.1109/TNNLS.2021.3070966 doi: 10.1109/TNNLS.2021.3070966
[24]	H. Li, C. Hu, G. Zhang, J. Hu, L. Wang, Fixed-/preassigned-time stabilization of delayed memristive neural networks, Inf. Sci., 610 (2022), 624–636. https://doi.org/10.1016/j.ins.2022.08.011 doi: 10.1016/j.ins.2022.08.011
[25]	Z. Yan, X. Huang, J. Cao, Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control, Sci. China Inf. Sci., 63 (2020), 212201. https://doi.org/10.1007/s11432-019-2664-7 doi: 10.1007/s11432-019-2664-7
[26]	R. Zhao, Z. Zuo, Y. Wang, Event-triggered control for networked switched systems with quantization, IEEE Trans. Syst. Man Cybern., 52 (2022), 6120–6128. https://doi.org/10.1109/TSMC.2021.3139386 doi: 10.1109/TSMC.2021.3139386
[27]	J. Ping, S. Zhu, M. Shi, S. Wu, M. Shen, X. Liu, et al., Event-triggered finite-time synchronization control for quaternion-valued memristive neural networks by an non-decomposition method, IEEE Trans. Network Sci. Eng., 10 (2023), 3609–3619. https://doi.org/10.1109/TNSE.2023.3268101 doi: 10.1109/TNSE.2023.3268101
[28]	J. Ping, S. Zhu, X. Liu, Finite/fixed-time synchronization of memristive neural networks via event-triggered control, Knowl. Based Syst., 258 (2022), 110013. https://doi.org/10.1016/j.knosys.2022.110013 doi: 10.1016/j.knosys.2022.110013
[29]	Y. Zhou, H. Zhang, Z. Zeng, Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control, Neural Networks, 139 (2021), 255–264. https://doi.org/10.1016/j.neunet.2021.02.029 doi: 10.1016/j.neunet.2021.02.029
[30]	N. Li, X. Wu, J. Feng, J. Lü, Fixed-time synchronization of complex dynamical networks: a novel and economical mechanism, IEEE Trans. Cybern., 52 (2022), 4430–4440. https://doi.org/10.1109/TCYB.2020.3026996 doi: 10.1109/TCYB.2020.3026996
[31]	S. Chen, Q. Song, Z. Zhao, Y. Liu, F. E. Alsaadi, Global asymptotic stability of fractional-order complex-valued neural networks with probabilistic time-varying delays, Neurocomputing, 450 (2021), 311–318. https://doi.org/10.1016/j.neucom.2021.04.043 doi: 10.1016/j.neucom.2021.04.043
[32]	J. Han, G. Chen, L. Wang, G. Zhang, J. Hu, Direct approach on fixed-time stabilization and projective synchronization of inertial neural networks with mixed delays, Neurocomputing, 535 (2023), 97–106. https://doi.org/10.1016/j.neucom.2023.03.038 doi: 10.1016/j.neucom.2023.03.038
[33]	A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb., 51 (1988), 99–128.
[34]	G. Zhang, Y. Shen, Q. Yin, J. Sun, Passivity analysis for memristor-based recurrent neural networks with discrete and distributed delays, Neural Networks, 61 (2015), 49–58. https://doi.org/10.1016/j.neunet.2014.10.004 doi: 10.1016/j.neunet.2014.10.004
[35]	E. Jiménez-Rodríguez, J. D. Sánchez-Torres, A. G. Loukianov, On optimal predefined-time stabilization, Int. J. Robust Nonlinear Control, 27 (2017), 3620–3642. https://doi.org/10.1002/rnc.3757 doi: 10.1002/rnc.3757
[36]	H. Khalil, Nonlinear systems, 3 Eds., Prentice Hall, 2002.
[37]	H. Jia, D. Luo, J. Wang, H. Shen, Fixed-time synchronization for inertial cohen–grossberg delayed neural networks: an event-triggered approach, Knowl. Based Syst., 250 (2022), 109104. https://doi.org/10.1016/j.knosys.2022.109104 doi: 10.1016/j.knosys.2022.109104
[38]	F. H. Clarke, Y. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth analysis and control theory, Springer Science & Business Media, 1998. https://doi.org/10.1007/b97650

Reader Comments

Your name:*

Email:*
© 2024 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)