Fixed-time control of switched memristor-based BAM neural networks with time-varying delays

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Abstract

This study investigates the prespecified-/finite-time stability for a class of memristor-based BAM neural networks (MBAMNNs) with discontinuity. By C-regular Lyapunov approach stability theories, some criteria are established to ensure that the switched MBAMNNs can achieve prespecified- /finite-time stabilization, which are independent of the initial states. Finally, some numerical examples demonstrate the effectiveness of the proposed criteria. This work provides a theoretical foundation for precise temporal control in complex neural networks.

Keywords

BAM neural networks / prespecified-time stability / finite-time stability / external input controller

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References

[1] L. Chua, Memristor-the missing circuit element, IEEE Trans. Circuit Theory, 18 (1971), 507-519. https://doi.org/10.1109/TCT.1971.1083337

[2] D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, The missing memristor found, Nature, 453 (2008), 80-83. https://doi.org/10.1038/nature06932

[3] M. Sharifi, Y. M. Banadaki, General SPICE models for memristor and application to circuit simulation of memristor-based synapses and memory cells, J. Circuits, Syst. Comput., 19 (2010), 407-424. https://doi.org/10.1142/S0218126610006141

[4] S. H. Jo, T. Chang, I. Ebong, B. B. Bhadviya, P. Mazumder, W. Lu, Nanoscale memristor device as synapse in neuromorphic systems, Nano Lett., 10 (2010), 1297-1301. https://doi.org/10.1021/nl904092h

[5] M. Jiang, S. Wang, J. Mei, Y. Shen, Finite-time synchronization control of a class of memristor-based recurrent neural networks, Neural Networks, 63 (2015), 133-140. https://doi.org/10.1016/j.neunet.2014.11.005

[6] C. D. Liang, M. F. Ge, Z. W. Liu, X. S. Zhan, J. H. Park, Predefined-time stabilization of T-S fuzzy systems: A novel integral sliding mode-based approach, IEEE Trans. Fuzzy Syst., 30 (2022), 4423-4433. https://doi.org/10.1109/TFUZZ.2022.3152834

[7] J. Xiao, Y. Li, S. Zhong, F. Xu, Extended dissipative state estimation for memristive neural networks with time-varying delay, ISA Trans., 64 (2016), 113-128. https://doi.org/10.1016/j.isatra.2016.05.007

[8] R. Zhang, D. Q. Zeng, S. M. Zhong, Y. G. Yu, Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays, Appl. Math. Comput., 310 (2017), 57-74. https://doi.org/10.1016/j.amc.2017.04.028

[9] G. Tan, W. H. Chen, J. Yang, X. Tran, Z. Li, Dual control for autonomous airborne source search with Nesterov accelerated gradient descent: Algorithm and performance analysis, Neurocomputing, 630 (2025), 129729. https://doi.org/10.1016/j.neucom.2025.129729

[10] G. Tan, T. Wang, A new result on H_∞ filtering criterion based on improved techniques , Circuits Syst. Signal Process., 2025. https://doi.org/10.1007/s00034-025-03305-4

[11] Y. Chen, C. Lu, X. Zhang, Allowable delay set flexible fragmentation approach to passivity analysis of delayed neural networks, Neurocomputing, 629 (2025), 129730. https://doi.org/10.1016/j.neucom.2025.129730

[12] B. Kosko, Bidirectional associative memories, IEEE Trans. Syst. Man Cybern., 18 (1988), 49-60. https://doi.org/10.1109/21.87054

[13] Y. P. Du, S. M. Zhong, N. Zhou, Global asymptotic stability of Markovian jumping stochastic Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays, Appl. Math. Comput., 243 (2014), 624-636. https://doi.org/10.1016/j.amc.2014.06.021

[14] H. B. Du, S. H. Li, C. J. Qian, Finite-time attitude tracking control of spacecraft with application to attitude synchronization, IEEE Trans. Autom. Control, 56 (2011), 2711-2717. https://doi.org/10.1109/TAC.2011.2159419

[15] Q. Lu, S. R. Liu, X. G. Xie, J. Wang, Decision making and finite-time motion control for a group of robots, IEEE Trans. Cybern., 43 (2013), 738-750. https://doi.org/10.1109/TSMCB.2012.2215318

[16] W. L. Lu, X. W. Liu, T. P. Chen, A note on finite-time and fixed-time stability, Neural Networks, 81 (2016), 11-15. https://doi.org/10.1016/j.neunet.2016.04.011

[17] W. J. Li, Y. J. Guan, J. D. Cao, F. Xu, A note on global stability of a degenerate diffusion avian influenza model with seasonality and spatial heterogeneity, Appl. Math. Lett., 148 (2024), 108884. https://doi.org/10.1016/j.aml.2023.108884

[18] W. J. Li, L. T. Zhang, J. D. Cao, F. Xu, Z. W. Cai, Finite time attractivity and exponential stability of a multi-stage epidemic system with discontinuous incidence, Qual. Theory Dyn. Syst., 24 (2025), 199. https://doi.org/10.1007/s12346-025-01358-z

[19] H. B. Zeng, Z. J. Zhu, S. P. Xiao, X. Zhang, A switched system model for exponential stability and dissipativity of delayed neural networks, IEEE Trans. Neural Networks Learn. Syst., 36 (2025), 19708-19717. https://doi.org/10.1109/TNNLS.2025.3590251

[20] A. Abdurahman, M. Abudusaimaiti, H. J. Jiang, Fixed/predefined-time lag synchronization of complex-valued BAM neural networks with stochastic perturbations, Appl. Math. Comput., 444 (2023), 127811. https://doi.org/10.1016/j.amc.2022.127811

[21] A. Abudireman, A. Abdurahman, Fixed-time synchronization of spatiotemporal fuzzy neural network via aperiodic intermittent control with hyperbolic sine function, J. Appl. Math. Comput., 71 (2025), 6651-6673. https://doi.org/10.1007/s12190-025-02569-y

[22] A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Trans. Autom. Control, 57 (2012), 2106-2110. https://doi.org/10.1109/TAC.2011.2179869

[23] F. C. Kong, H. L. Ni, Q. X. Zhu, C. Hu, T. W. Huang, Fixed-time and predefined-time synchronization of discontinuous neutral-type competitive networks via non-chattering adaptive control strategy, IEEE Trans. Network Sci. Eng., 10 (2023), 3644-3657. https://doi.org/10.1109/TNSE.2023.3271109

[24] S. Z. Xie, Q. Chen, Predefined-time disturbance estimation and attitude control for rigid spacecraft, IEEE Trans. Circuits Syst. II Express Briefs, 71 (2024), 2089-2093. https://doi.org/10.1109/TCSII.2023.3331825

[25] E. Jimenez-Rodriguez, A. J. Munoz-Vazquez, J. D. Sanchez-Torres, M. Defoort, A. G. Loukianov, Lyapunov-like characterization of predefined-time stability, IEEE Trans. Autom. Control, 65 (2020), 4922-4927. https://doi.org/10.1109/TAC.2020.2967555

[26] J. D. Sanchez-Torres, D. Gomez-Gutierrez, E. Lopez, A. G. Loukianov, A class of predefined-time stable dynamical systems, IMA J. Math. Control Inf., 35 (2018), i1-i29. https://doi.org/10.1093/imamci/dnx004

[27] C. Hu, H. B. He, H. J. Jiang, Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability, IEEE Trans. Cybern., 51 (2021), 2882-2892. https://doi.org/10.1109/TCYB.2020.2977934

[28] C. Hu, H. J. Jiang, Special functions-based fixed-time estimation and stabilization for dynamic systems, IEEE Trans. Syst. Man Cybern.: Syst., 52 (2022), 3251-3262. https://doi.org/10.1109/TSMC.2021.3062206

[29] Y. Wang, Y. Song, D. J. Hill, M. Krstic, Prescribed-time consensus and containment control of networked multiagent systems, IEEE Trans. Cybern., 49 (2019), 1138-1147. https://doi.org/10.1109/TCYB.2017.2788874

[30] E. Jimenez-Rodriguez, J. D. Sanchez-Torres, D. Gomez-Gutierrez, A. G. Loukianov, Variable structure predefined-time stabilization of second-order systems, Asian J. Control, 21 (2019), 1179-1188. https://doi.org/10.1002/asjc.1785

[31] E. Jimenez-Rodriguez, J. D. Sanchez-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

[32] B. Li, L. Zhao, S. Wen, Periodic event-triggered consensus of stochastic multi-agent systems under switching topology, Artif. Intell. Sci. Eng., 1 (2025), 147-156. https://doi.org/10.23919/AISE.2025.000011

[33] S. S. Zhao, L. H. Zhao, S. P. Wen, Secure synchronization control of Markovian jump neural networks under DoS attacks with memory-based adaptive event-triggered mechanism, Artif. Intell. Sci. Eng., 1 (2025), 64-78. https://doi.org/10.23919/AISE.2025.000006

[34] H. C. Lin, H. B. Zeng, X. M. Zhang, W. Wang, Stability analysis for delayed neural networks via a generalized reciprocally convex inequality, IEEE Trans. Neural Networks Learn. Syst., 34 (2022), 7491-7499. https://doi.org/10.1109/TNNLS.2022.3144032

[35] Z. Y. Guo, L. L. Liu, J. Wang, Multistability of switched neural networks with piecewise linear activation functions under state-dependent switching, IEEE Trans. Neural Networks Learn. Syst., 30 (2019), 2052-2066. https://doi.org/10.1109/TNNLS.2018.2876711

[36] Z. Y. Guo, L. L. Liu, J. Wang, Multistability of recurrent neural networks with piecewise-linear radial basis functions and state-dependent switching parameters, IEEE Trans. Syst. Man Cybern.: Syst., 50 (2020), 4458-4471. https://doi.org/10.1109/TSMC.2018.2853138

[37] C. Chen, L. Li, H. Peng, Y. Yang, Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay, Neural Networks, 96 (2017), 47-54. https://doi.org/10.1016/j.neunet.2017.08.012

[38] L. M. Wang, Y. Shen, G. D. Zhang, Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control, IEEE Trans. Cybern., 46 (2016), 2300-2310. https://doi.org/10.1109/TCYB.2015.2475277

[39] S. P. Wen, Z. G. Zeng, T. W. Huang, Q. G. Meng, W. Yao, Lag synchronization of switched neural networks via neural activation function and applications in image encryption, IEEE Trans. Neural Networks Learn. Syst., 26 (2015), 1493-1502. https://doi.org/10.1109/TNNLS.2014.2387355

[40] S. P. Wen, Z. G. Zeng, M. Chen, T. W. Huang, Synchronization of switched neural networks with communication delays via the event-triggered control, IEEE Trans. Neural Networks Learn. Syst., 28 (2017), 2334-2343. https://doi.org/10.1109/TNNLS.2016.2580609

[41] K. Mathiyalagan, J. H. Park, R. Sakthivel, Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities, Appl. Math. Comput., 259 (2015), 967-979. https://doi.org/10.1016/j.amc.2015.03.022

[42] R. Sakthivel, R. Anbuvithya, K. Mathiyalagan, Y. K. Ma, P. Prakash, Reliable anti-synchronization conditions for BAM memristive neural networks with different memductance functions, Appl. Math. Comput., 275 (2016), 213-228. https://doi.org/10.1016/j.amc.2015.11.060

[43] Z. Cai, L. H. Huang, Generalized Lyapunov approach for functional differential inclusions, Automatica, 113 (2020), 108740. https://doi.org/10.1016/j.automatica.2019.108740

[44] Z. Cai, J. Huang, L. H. Huang, Generalized Lyapunov-Razumikhin method for retarded differential inclusions: Applications to discontinuous neural networks, Discrete Contin. Dyn. Syst. - Ser. B, 22 (2017), 3591-3614. https://doi.org/10.3934/dcdsb.2017181

[45] Z. Cai, L. H. Huang, Lyapunov-Krasovskii stability analysis of delayed Filippov system: Applications to neural networks with switching control, Int. J. Robust Nonlinear Control, 30 (2020), 699-718. https://doi.org/10.1002/rnc.4787

[46] Z. Cai, L. H. Huang, Z. Wang, Finite-/Fixed-time stability of nonautonomous functional differential inclusion: Lyapunov approach involving indefinite derivative, IEEE Trans. Neural Networks Learn. Syst., 33 (2021), 6763-6774. https://doi.org/10.1109/TNNLS.2021.3083396

[47] Z. Y. Guo, L. H. Huang, Generalized Lyapunov method for discontinuous systems, Nonlinear Anal. Theory Methods Appl., 71 (2009), 3083-3092. https://doi.org/10.1016/j.na.2009.01.220

[48] J. Cortés, Discontinuous dynamical systems, IEEE Control Syst. Mag., 28 (2008), 36-73. https://doi.org/10.1109/MCS.2008.919306

[49] Q. X. Zhu, J. D. Cao, Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays, IEEE Trans. Neural Networks Learn. Syst., 23 (2012), 467-479. https://doi.org/10.1109/TNNLS.2011.2182659

[50] M. Forti, M. Grazzini, P. Nistri, L. Pancioni, Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations, Physica D, 214 (2006), 88-99. https://doi.org/10.1016/j.physd.2005.12.006

[51] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities , Cambridge University Press, Cambridge, 1952.

[52] Z. Cai, L. H. Huang, Z. Wang, Prespecified-time control of switched neural networks: novel Lyapunov approach of prespecified-time stability, Comput. Appl. Math., 43 (2024), 224. https://doi.org/10.1007/s40314-024-02748-w

[53] J. P. Aubin, A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory , Springer-Verlag, 1984.