Fixed-Time and Predefined-Time Synchronization of Inertial Memristive Neural Networks With Proportional Delay and Mismatched Switching Jumps via Stochastic Particle Swarm Optimization

Qiang Lai; Jun Wang; Leimin Wang; Minghong Qin

doi:10.1109/JAS.2025.126008

Volume 13 Issue 6

Jun. 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

CiteScore: 28.2, Top 1% (Q1)
Google Scholar h5-index: 95， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(6): 1274-1287

Q. Lai, J. Wang, L. Wang, and M. Qin, “Fixed-time and predefined-time synchronization of inertial memristive neural networks with proportional delay and mismatched switching jumps via stochastic particle swarm optimization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1274–1287, Jun. 2026. doi: 10.1109/JAS.2025.126008

Citation:

Q. Lai, J. Wang, L. Wang, and M. Qin, “Fixed-time and predefined-time synchronization of inertial memristive neural networks with proportional delay and mismatched switching jumps via stochastic particle swarm optimization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1274–1287, Jun. 2026. doi: 10.1109/JAS.2025.126008

Citation:

Q. Lai, J. Wang, L. Wang, and M. Qin, “Fixed-time and predefined-time synchronization of inertial memristive neural networks with proportional delay and mismatched switching jumps via stochastic particle swarm optimization,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1274–1287, Jun. 2026. doi: 10.1109/JAS.2025.126008

PDF( 1866 KB)

Fixed-Time and Predefined-Time Synchronization of Inertial Memristive Neural Networks With Proportional Delay and Mismatched Switching Jumps via Stochastic Particle Swarm Optimization

doi: 10.1109/JAS.2025.126008

Funds: This work was supported by the National Natural Science Foundation of China (62366014, 62473348) and Jiangxi Provincial Natural Science Foundation (20252BAC250013)

More Information

Author Bio:
Qiang Lai (Senior Member, IEEE) received the Ph.D. degree in control theory and control engineering from Huazhong University of Science and Technology in 2014. He is currently a Professor of the School of Electrical and Automation Engineering, East China Jiaotong University. He has been selected as World’s Top 2% Scientists in 2020−2025 ranking of Stanford University. He has authored more than 150 journal articles, and served as Associate Editor, Editorial Board Member, Guest Editor of 10 SCI journals. His research interests include nonlinear dynamics, information security, complex networks, multi-agent systems, and artificial intelligence

Jun Wang is currently pursuing the M.Sc. degree in control science and control engineering from the East China Jiaotong University. He has authored several SCI journal articles and served as Reviewer for several international journals. His research interests include chaos theory and application, synchronization control, and memristive neural networks

Leimin Wang (Senior Member, IEEE) received the Ph.D. degree in control science and engineering from Huazhong University of Science and Technology in 2016. From 2018 to 2019, he was a Visiting Scholar with the Department of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Kingston, USA. He is currently a Professor with the School of Artificial Intelligence and Automation, China University of Geosciences. His current research interests include neural networks, memristive systems, and finite-time control

Minghong Qin is currently pursuing the M.Sc. degree in electronic and information engineering from East China Jiaotong University. He has authored more than 10 SCI journal articles and served as Reviewer for several international journals. His research interests include nonlinear dynamics, chaos-based applications, neural networks, and memristive systems and circuits
Corresponding author: Qiang Lai, e-mail: chaos1963@ecjtu.edu.cn
Received Date: 2025-05-14
Revised Date: 2025-09-10
Accepted Date: 2025-10-24

Abstract

Abstract

This paper studies the fixed-time synchronization (FxTS) and predefined-time synchronization (PTS) of a class of inertial memristive neural networks (IMNNs), which have unbounded proportional delay independent of time linearity and mismatched switching jump coefficients. Based on Filippov solution theory and Lyapunov methods, this work develops an enhanced FxTS criterion delivering a tighter upper bound on convergence time and thereby extending guaranteed fixed‐time behavior to a wider range of networks. A refined PTS condition that incorporates additional state-dependent terms accelerates error decay and reduces conservatism during the transient response. Numerical simulations show that the convergence rate of PTS under this strategy is significantly improved. Moreover, an optimization model with minimum control energy and dynamic error as objective functions is proposed to obtain more accurate controller parameters, and the stochastic inertia weight particle swarm optimization (SIWPSO) algorithm is introduced to solve the optimization model. Numerical studies not only validate the theoretical results for both FxTS and PTS but also demonstrate a secure communication application in which the chaos of the IMNNs acts as a masking carrier and enables perfect encryption and decryption of a complex test signal through SIWPSO-optimized FxTS and PTS.

FullText(HTML)

References(43)

References

[1]	R. Guo, S. Xu, B. Zhang, and Q. Ma, “Nonfragile exponential synchronization for delayed fuzzy memristive inertial neural networks via memory sampled-data control,” IEEE Trans. Fuzzy Syst., vol. 32, no. 6, pp. 3825–3837, Jun. 2024. doi: 10.1109/TFUZZ.2024.3386215
[2]	X. Liu, H. He, and J. Cao, “Event-triggered bipartite synchronization of delayed inertial memristive neural networks with unknown disturbances,” IEEE Trans. Control Netw. Syst., vol. 11, no. 3, pp. 1408–1419, Sep. 2024. doi: 10.1109/TCNS.2023.3338256
[3]	Q. Lai, L. Yang, G. Hu, Z.-H. Guan, and H. H.-C. Iu, “Constructing multiscroll memristive neural network with local activity memristor and application in image encryption,” IEEE Trans. Cybern., vol. 54, no. 7, pp. 4039–4048, Jul. 2024. doi: 10.1109/TCYB.2024.3377011
[4]	Q. Lai and L. Yang, “Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors,” Chaos, Solitons Fractals, vol. 174, Art. no. 113807, Sep. 2023. doi: 10.1016/j.chaos.2023.113807
[5]	G. Zhang and S. Wen, “New approximate results of fixed-time stabilization for delayed inertial memristive neural networks,” IEEE Trans. Circuits Syst. II: Express Briefs, vol. 71, no. 7, pp. 3428–3432, Jul. 2024. doi: 10.1109/TCSII.2024.3361670
[6]	L. Wang, Y. Hu, C. Hu, Y. Zhou, and S. Wen, “Finite-time synchronization of delayed fuzzy inertial neural networks via intermittent control,” Neurocomputing, vol. 574, Art. no. 127288, Mar. 2024. doi: 10.1016/j.neucom.2024.127288
[7]	Q. Liu, H. Yan, H. Zhang, C. Chen, and Y. Chang, “Exponential synchronization of second-order fuzzy memristor-based neural networks with mixed time delays via fuzzy adaptive control,” IEEE Trans. Fuzzy Syst., vol. 31, no. 6, pp. 1953–1965, Jun. 2023. doi: 10.1109/TFUZZ.2022.3216777
[8]	C. Ma and D. Dong, “Finite-time prescribed performance time-varying formation control for second-order multi-agent systems with non-strict feedback based on a neural network observer,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 1039–1050, Apr. 2024. doi: 10.1109/JAS.2023.123615
[9]	J. Liu, S. Li, and R. Liu, “Recurrent neural network inspired finite-time control design,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 6, pp. 1527–1529, Jun. 2024. doi: 10.1109/JAS.2023.123297
[10]	D. Huang, M. Jiang, and J. Jian, “Finite-time synchronization of inertial memristive neural networks with time-varying delays via sampled-date control,” Neurocomputing, vol. 266, pp. 527–539, Nov. 2017. doi: 10.1016/j.neucom.2017.05.075
[11]	Z. Guo, S. Gong, and T. Huang, “Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control,” Neurocomputing, vol. 293, pp. 100–107, Jun. 2018. doi: 10.1016/j.neucom.2018.03.004
[12]	A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Trans. Autom. Contr., vol. 57, no. 8, pp. 2106–2110, Aug. 2012. doi: 10.1109/TAC.2011.2179869
[13]	C. Chen, L. Li, H. Peng, and Y. Yang, “Fixed-time synchronization of inertial memristor-based neural networks with discrete delay,” Neural Netw., vol. 109, pp. 81–89, Jan. 2019. doi: 10.1016/j.neunet.2018.10.011
[14]	R. Wei and J. Cao, “Synchronization analysis of inertial memristive neural networks with time-varying delays,” J. Artif. Intell. Soft Comput. Res., vol. 8, no. 4, pp. 269–282, Oct. 2018. doi: 10.1515/jaiscr-2018-0017
[15]	B. Ning, Q.-L. Han, and L. Ding, “A brief overview of recent advances in distributed accelerated secondary control for islanded AC microgrids,” IEEE Trans. Industr. Inform., vol. 21, no. 9, pp. 6605–6614, Sep. 2025. doi: 10.1109/TII.2025.3570749
[16]	Q. Lai, Y. Liu, F. Liu, and X. Zhao, “Generating grid multiscroll memristive Chua’s circuit and its predefined-time synchronization for secure communication,” IEEE Trans. Circuits Syst. I: Regul. Pap., vol. 72, no. 10, pp. 5947–5956, Oct. 2025. doi: 10.1109/TCSI.2025.3541635
[17]	Q. Tang, S. Qu, C. Zhang, Z. Tu, and Y. Cao, “Effects of impulse on prescribed-time synchronization of switching complex networks,” Neural Netw., vol. 174, Art. no. 106248, Jun. 2024. doi: 10.1016/j.neunet.2024.106248
[18]	Q. Gan, L. Li, J. Yang, Y. Qin, and M. Meng, “Improved results on fixed-/preassigned-time synchronization for memristive complex-valued neural networks,” IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 10, pp. 5542–5556, Oct. 2022. doi: 10.1109/TNNLS.2021.3070966
[19]	S. Chen, Y. Wan, and J. Cao, “Predefined-time synchronization for FitzHugh-Nagumo neural networks with external disturbances and multiple time scales: An adaptive control approach,” IEEE Trans. Autom. Sci. Eng., vol. 22, pp. 7080−7091, Oct. 2025.
[20]	N. Zhao, Y. Qiao, J. Miao, and L. Duan, “Fixed-time synchronization of impulsive octonion-valued fuzzy inertial neural networks via improving fixed-time stability,” IEEE Trans. Fuzzy Syst., vol. 32, no. 4, pp. 1978–1990, Apr. 2024. doi: 10.1109/TFUZZ.2023.3339162
[21]	X. Hu, L. Wang, Y. Sheng, Q. Xiao, and M.-F. Ge, “Impulsive fixed-time bipartite synchronization of fuzzy multilayer signed networks,” IEEE Trans. Fuzzy Syst., vol. 33, no. 3, pp. 1049–1059, Mar. 2025. doi: 10.1109/TFUZZ.2024.3505210
[22]	K. Tu, Y. Xue, and X. Zhang, “Observer-based resilient dissipativity control for discrete-time memristor-based neural networks with unbounded or bounded time-varying delays,” Neural Netw., vol. 175, Art. no. 106279, Jul. 2024. doi: 10.1016/j.neunet.2024.106279
[23]	Z. Zhang, K. Zhang, X. Xie, and V. Stojanovic, “ADP-based prescribed-time control for nonlinear time-varying delay systems with uncertain parameters,” IEEE Trans. Autom. Sci. Eng., vol. 22, pp. 3086−3096, Apr. 2025.
[24]	J. Lei, Y.-X. Li, and S. Tong, “Fuzzy adaptive distributed optimization of uncertain multiagent systems with time-varying delays,” IEEE Trans. Fuzzy Syst., vol. 32, no. 11, pp. 6125–6135, Nov. 2024. doi: 10.1109/TFUZZ.2024.3441008
[25]	X. Wang, X. Liang, X. Zhang, and Y. Xue, “L_p synchronization of shunting inhibitory cellular neural networks with multiple proportional delays,” Inf. Sci., vol. 654, Art. no. 119865, Jan. 2024. doi: 10.1016/j.ins.2023.119865
[26]	Y. Wan, L. Zhou, and J. Han, “Global polynomial synchronization of proportional delay memristive neural networks with uncertain parameters and its application to image encryption,” Eng. Appl. Artif. Intell., vol. 147, Art. no. 110290, May 2025. doi: 10.1016/j.engappai.2025.110290
[27]	W. Yang, J. Huang, X. He, S. Wen, and T. Huang, “Finite-time synchronization of neural networks with proportional delays for RGB-D image protection,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 6, pp. 8149–8160, Jun. 2024. doi: 10.1109/TNNLS.2022.3225164
[28]	A. Kumar, S. Singh, S. Das, and Y. Cao, “Projective quasi-synchronization of complex-valued recurrent neural networks with proportional delay and mismatched parameters via matrix measure approach,” Eng. Appl. Artif. Intell., vol. 126, Art. no. 106800, Nov. 2023. doi: 10.1016/j.engappai.2023.106800
[29]	H. Lin, X. Deng, F. Yu, and Y. Sun, “Grid multibutterfly memristive neural network with three memristive systems: Modeling, dynamic analysis, and application in police IoT,” IEEE Internet Things J., vol. 11, no. 18, pp. 29878–29889, Sep. 2024. doi: 10.1109/JIOT.2024.3409373
[30]	D. Luo, C. Wang, Q. Deng, and Y. Sun, “Dynamics in a memristive neural network with three discrete heterogeneous neurons and its application,” Nonlinear Dyn., vol. 113, pp. 5811–5824, Mar. 2025. doi: 10.1007/s11071-024-10513-1
[31]	L. Wang and C.-K. Zhang, “Exponential synchronization of memristor-based competitive neural networks with reaction- diffusions and infinite distributed delays,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 1, pp. 745–758, Jan. 2024. doi: 10.1109/TNNLS.2022.3176887
[32]	L. Wang, S. Jiang, M.-F. Ge, C. Hu, and J. Hu, “Finite-/fixed-time synchronization of memristor chaotic systems and image encryption application,” IEEE Trans. Circuits Syst. I: Regul. Pap., vol. 68, no. 12, pp. 4957–4969, Dec. 2021. doi: 10.1109/TCSI.2021.3121555
[33]	C. Gong, N. Zhou, S. Xia, and S. Huang, “Quantum particle swarm optimization algorithm based on diversity migration strategy,” Future Gener. Comput. Syst., vol. 157, pp. 445–458, Aug. 2024. doi: 10.1016/j.future.2024.04.008
[34]	Z. Lei, S. Gao, Z. Zhang, H. Yang, and H. Li, “A chaotic local search-based particle swarm optimizer for large-scale complex wind farm layout optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1168–1180, May 2023. doi: 10.1109/JAS.2023.123387
[35]	J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. ICNN'95-Int. Conf. Neural Networks, Perth, Australia, 1995, pp. 1942−1948.
[36]	A. Nickabadi, M. M. Ebadzadeh, and R. Safabakhsh, “A novel particle swarm optimization algorithm with adaptive inertia weight,” Appl. Soft Comput., vol. 11, pp. 3658–3670, Jun. 2011. doi: 10.1016/j.asoc.2011.01.037
[37]	H. Yan, Y. Qiao, Z. Ren, L. Duan, and J. Miao, “Quantized control for predefined-time synchronization of inertial memristive neural networks,” Neural Comput. Appl., vol. 36, no. 12, pp. 6497–6512, Jan. 2024. doi: 10.1007/s00521-023-09371-6
[38]	Y. Jiang, S. Zhu, M. Shen, S. Wen, and C. Mu, “Aperiodically intermittent control approach to finite-time synchronization of delayed inertial memristive neural networks,” IEEE Trans. Artif. Intell., vol. 6, no. 4, pp. 1014–1023, Apr. 2025. doi: 10.1109/TAI.2024.3507740
[39]	A. F. Filippov, Differential Equations with Discontinuous Righthand Sides: Control Systems. Dordrecht, The Netherlands: Springer, 1988.
[40]	M. Zhang, H. Zang, and L. Bai, “A new predefined-time sliding mode control scheme for synchronizing chaotic systems,” Chaos, Solitons Fractals, vol. 164, Art. no. 112745, Nov. 2022. doi: 10.1016/j.chaos.2022.112745
[41]	W. Zou, P. Shi, Z. Xiang, and Y. Shi, “Finite-time consensus of second-order switched nonlinear multi-agent systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 5, pp. 1757–1762, May 2020. doi: 10.1109/TNNLS.2019.2920880
[42]	B. Ning, Q.-L. Han, Z. Zuo, and L. Ding, “Accelerated secondary frequency regulation and active power sharing for islanded microgrids with external disturbances: A fully distributed approach,” Automatica, vol. 174, Art. no. 112146, Apr. 2025. doi: 10.1016/j.automatica.2025.112146
[43]	J. Xiao, Y. Hu, Z. Zeng, A. Wu, and S. Wen, “Fixed/predefined-time synchronization of memristive neural networks based on state variable index coefficient,” Neurocomputing, vol. 560, Art. no. 126849, Dec. 2023. doi: 10.1016/j.neucom.2023.126849