Fault-resilient output-feedback control of delayed memristor-based neural networks with dual performance guarantees

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Abstract

This work investigated the fault-resilient output-feedback control problem for delayed memristor-based neural networks (MBNNs) subject to actuator faults and external disturbances. To overcome the practical limitation that full-state measurements are often unavailable, an output-feedback controller was designed to rely solely on measurable outputs. By constructing a Lyapunov-Krasovskii functional and employing the Bessel-Legendre inequality together with the generalized reciprocally convex combination inequality, a sufficient condition was established to simultaneously guarantee $\mathcal{H}_{\infty}$ and $\mathcal{L}_{2}-\mathcal{L}_{\infty}$ disturbance attenuation for the considered MBNNs. Decoupling techniques were then introduced to eliminate nonlinear coupling terms, and the controller synthesis was formulated in terms of linear matrix inequalities that are solvable with existing convex optimization tools. Finally, a numerical example was provided to corroborate the reduced conservatism of the proposed analysis condition and the effectiveness of the synthesis method in achieving the desired dual-performance guarantees.

Keywords

memristor-based neural network / fault-resilient control / output-feedback control / $\mathcal{H}_{\infty}$ performance / $\mathcal{L}_{2}-\mathcal{L}_{\infty}$ performance

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References

[1] G. Tian, Y. Yang, S. Wen, Time-series stock price forecasting based on neural networks: A comprehensive survey, Artif. Intell. Sci. Eng., 1 (2025), 255-277. https://doi.org/10.23919/AISE.2025.000018

[2] Q. Liu, H. Yan, H. Zhang, L. Zeng, C. Chen, Adaptive intermittent pinning control for synchronization of delayed nonlinear memristive neural networks with reaction-diffusion items, IEEE Trans. Neural Networks Learn. Syst., 36 (2024), 2234-2245. https://doi.org/10.1109/TNNLS.2023.3344515

[3] X. Geng, J. Feng, Y. Zhao, N. Li, J. Wang, Fixed-time synchronization of nonlinear coupled memristive neural networks with time delays via sliding-mode control, Electron. Res. Arch., 31 (2023), 3291-3308. https://doi.org/10.3934/era.2023166

[4] Y. Fan, X. Huang, Z. Wang, Memory-dependent event-trigger scheme for secure control of memristive neural networks: Dealing with deception attacks, IEEE Trans. Ind. Inf., 20 (2023), 5562-5571. https://doi.org/10.1109/TII.2023.3335996

[5] X. Zhang, J. Lu, Z. Wang, R. Wang, J. Wei, T. Shi, et al., Hybrid memristor-CMOS neurons for in-situ learning in fully hardware memristive spiking neural networks, Sci. Bull., 66 (2021), 1624-1633. https://doi.org/10.1016/j.scib.2021.04.014

[6] H. Lin, C. Wang, Q. Hong, Y. Sun, A multi-stable memristor and its application in a neural network, IEEE Trans. Circuits Syst. II, Exp. Briefs, 67 (2020), 3472-3476. https://doi.org/10.1109/TCSII.2020.3000492

[7] E. Wang, B. Hu, Z. H. Guan, Chaotic dynamics and synchronization of multi-region neural network based on locally active memristor, Chaos, Solitons Fractals, 197 (2025), 116437. https://doi.org/10.1016/j.chaos.2025.116437

[8] L. Yang, J. Zhang, Memristor-coupled heterogeneous Hopfield neural network with switchable activation functions and its synchronization control, Chaos, Solitons Fractals, 200 (2025), 117101. https://doi.org/10.1016/j.chaos.2025.117101

[9] S. G. Hu, Y. Liu, Z. Liu, T. P. Chen, J. J. Wang, Q. Yu, et al., Associative memory realized by a reconfigurable memristive Hopfield neural network, Nat. Commun., 6 (2015), 7522. https://doi.org/10.1038/ncomms8522

[10] C. Xu, M. Liao, C. Wang, J. Sun, H. Lin, Memristive competitive Hopfield neural network for image segmentation application, Cogn. Neurodyn., 17 (2023), 1061-1077. https://doi.org/10.1007/s11571-022-09891-2

[11] S. A. Thomas, R. Sharma, D. M. Das, Analyzing the impact of parasitics on a CMOS-memristive crossbar neural network based on winner-take-all and Hebbian rule, Mem.-Mater. Devices Circuits Syst., 5 (2023), 100081. https://doi.org/10.1016/j.memori.2023.100081

[12] S. Zhang, X. Peng, X. Wang, C. Chen, Z. Zeng, A novel memristive multiscroll multistable neural network with application to secure medical image communication, IEEE Trans. Circuits Syst. Video Technol., 35 (2024), 1774-1786. https://doi.org/10.1109/TCSVT.2024.3483569

[13] H. Peng, L. Gan, X. Guo, Memristor-based spiking neural networks: Cooperative development of neural network architecture/algorithms and memristors, Chip, 3 (2024), 100093. https://doi.org/10.1016/j.chip.2024.100093

[14] Z. Yan, X. Huang, J. Liang, Aperiodic sampled-data control for stabilization of memristive neural networks with actuator saturation: A dynamic partitioning method, IEEE Trans. Cybern., 53 (2022), 1725-1737. https://doi.org/10.1109/TCYB.2021.3108805

[15] Z. Wang, L. Yan, Y. Fan, F. Wang, H. Shen, Switching event-triggered-based gain-scheduled control for bipartite synchronization of coupled coopetitive memristive neural networks, IEEE Trans. Syst. Man Cybern. Syst., 55 (2025), 6951-6963. https://doi.org/10.1109/TSMC.2025.3594542

[16] X. Si, Z. Wang, X. Huang, M. Xiao, Finite-time bipartite synchronization of delayed antagonistic memristive neural networks: Optimizing event-triggered controller parameters, IEEE Trans. Artif. Intell., 2026. https://doi.org/10.1109/TAI.2025.3650558

[17] Z. Yang, B. Zhao, D. Liu, Synchronization of delayed memristor-based neural networks via pinning control with local information, IEEE Trans. Neural Networks Learn. Syst., 35 (2023), 13619-13630. https://doi.org/10.1109/TNNLS.2023.3270345

[18] C. Yang, J. Wu, Z. Qiao, An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach, Electron. Res. Arch., 31 (2023), 2428-2446. https://doi.org/10.3934/era.2023123

[19] Z. Yan, D. Zuo, T. Guo, J. Zhou, Quantized H_∞ stabilization for delayed memristive neural networks , Neural Comput. Appl., 35 (2023), 16473-16486. https://doi.org/10.1007/s00521-023-08510-3

[20] S. Lin, X. Liu, Y. Huang, Event-triggered synchronization and H_∞ synchronization of coupled delayed reaction-diffusion memristive neural networks , Math. Methods Appl. Sci., 46 (2023), 9079-9102. https://doi.org/10.1002/mma.9039

[21] Y. Huang, A. Li, General decay anti-synchronization and H_∞ anti-synchronization of derivative coupled delayed memristive neural networks with constant and delayed state coupling , Commun. Nonlinear Sci. Numer. Simul., 139 (2024), 108313. https://doi.org/10.1016/j.cnsns.2024.108313

[22] J. Wang, T. Ru, H. Shen, J. Cao, J. H. Park, Finite-time L₂-L_∞ synchronization for semi-Markov jump inertial neural networks using sampled data , IEEE Trans. Network Sci. Eng., 8 (2020), 163-173. https://doi.org/10.1109/TNSE.2020.3032025

[23] J. Wang, Y. Zhu, L₂-L_∞ control for memristive NNs with non-necessarily differentiable time-varying delay , Math. Biosci. Eng., 20 (2023), 13182-13199. https://doi.org/10.3934/mbe.2023588

[24] Z. Xu, J. Ren, X. Zhou, J. Yao, Adaptive prescribed performance output feedback control for full-state-constrained DC motors subject to uncertainties and input saturation, Eur. J. Control, 77 (2024), 100961. https://doi.org/10.1016/j.ejcon.2024.100961

[25] W. Zhang, G. Zong, B. Niu, X. Zhao, N. Xu, Adaptive fuzzy dynamic event-triggered control for PDE-ODE cascaded systems with actuator failures, Fuzzy Sets Syst., 519 (2025), 109514. https://doi.org/10.1016/j.fss.2025.109514

[26] D. Grande, A. Peruffo, G. Salavasidis, E. Anderlini, D. Fenucci, A. B. Phillips, et al., Passive fault-tolerant augmented neural Lyapunov control: A method to synthesise control functions for marine vehicles affected by actuators faults, Control Eng. Pract., 148 (2024), 105935. https://doi.org/10.1016/j.conengprac.2024.105935

[27] J. Zhang, H. Xia, Y. Zhu, Y. Fu, Research on sensor fault tolerance technology in nuclear power plant control system, Ann. Nucl. Energy, 207 (2024), 110714. https://doi.org/10.1016/j.anucene.2024.110714

[28] P. Zhu, S. Jin, X. Bu, Z. Hou, Distributed data-driven event-triggered fault-tolerant control for a connected heterogeneous vehicle platoon with sensor faults, IEEE Trans. Intell. Transp. Syst., 25 (2023), 5498-5509. https://doi.org/10.1109/TITS.2023.3335227

[29] F. Jia, F. Cao, X. He, Active fault-tolerant control against intermittent faults for state-constrained nonlinear systems, IEEE Trans. Syst. Man Cybern. Syst., 54 (2024), 2389-2401. https://doi.org/10.1109/TSMC.2023.3344292

[30] X. Liu, Z. Yuan, Z. Gao, W. Zhang, Reinforcement learning-based fault-tolerant control for quadrotor UAVs under actuator fault, IEEE Trans. Ind. Inf., 20 (2024), 13926-13935. https://doi.org/10.1109/TII.2024.3438241

[31] J. Zhou, X. Ma, Z. Yan, C. K. Ahn, Fault-tolerant reduced-order asynchronous networked filtering of 2-D Bernoulli jump systems, IEEE Trans. Syst. Man Cybern. Syst., 54 (2023), 891-902. https://doi.org/10.1109/TSMC.2023.3321047

[32] Y. Liu, X. Zhao, J. H. Park, F. Fang, Fault-tolerant control for TS fuzzy systems with an aperiodic adaptive event-triggered sampling, Fuzzy Sets Syst., 452 (2023), 23-41. https://doi.org/10.1016/j.fss.2022.04.019

[33] J. Liu, J. Dong, Fault-tolerant consensus control with privacy-preserving virtual layer for heterogeneous multi-agent system, IEEE Trans. Autom. Sci. Eng., 22 (2024), 5687-5699. https://doi.org/10.1109/TASE.2024.3428408

[34] Z. Du, Y. Lyu, Z. Wu, J. Zhu, Z. Liu, Y. Yang, Fault-tolerant control based on dynamic regressor extension and mixing and adaptive allocation for fixed-wing aircraft with asymmetric damage, IEEE Trans. Aerosp. Electron. Syst., 61 (2025), 9774-9789. https://doi.org/10.1109/TAES.2025.3558180

[35] M. Jamali, H. R. Baghaee, M. S. Sadabadi, G. B. Gharehpetian, A. Anvari-Moghaddam, F. Blaabjerg, Distributed finite-time fault-tolerant control of isolated AC microgrids considering input constraints, IEEE Trans. Smart Grid, 13 (2022), 4525-4537. https://doi.org/10.1109/TSG.2022.3188199

[36] J. Zhou, Y. Liu, J. Xia, Z. Wang, S. Arik, Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters, Neural Networks, 125 (2020), 194-204. https://doi.org/10.1016/j.neunet.2020.02.015

[37] D. Chen, K. Shi, O. Kwon, X. Cai, Y. Sun, S. Wen, et al., Fault-tolerant impulsive synchronization in hypercomplex neural networks via AI-driven adaptive switching mechanism, Commun. Nonlinear Sci. Numer. Simul., 153 (2026), 109511. https://doi.org/10.1016/j.cnsns.2025.109511

[38] T. Radhika, A. Chandrasekar, Y. C. Lee, A. R. Subhashri, M. A. Shamrooz, W. J. Chang, Fault-tolerant state estimation synthesis for competitive neural networks subject to deception attacks using probabilistic time varying delay, J. Franklin Inst., 363 (2026), 108679. https://doi.org/10.1016/j.jfranklin.2026.108679

[39] Z. Du, J. Zhu, H. Wang, Stability criteria for memristor-based generalized neural networks with time-varying delay via an improved integral inequality, Nonlinear Dyn., 113 (2025), 1745-1759. https://doi.org/10.1007/s11071-024-10313-7

[40] G. Chen, J. Xia, J. H. Park, H. Shen, G. Zhuang, Sampled-data synchronization of stochastic Markovian jump neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., 33 (2022), 3829-3841. https://doi.org/10.1109/TNNLS.2021.3054615

[41] G. Zhuang, J. Xia, J. E. Feng, Y. Wang, G. Chen, Dynamic compensator design and H_∞ admissibilization for delayed singular jump systems via Moore-Penrose generalized inversion technique , Nonlinear Anal. Hybrid Syst., 49 (2023), 101361. https://doi.org/10.1016/j.nahs.2023.101361

[42] J. Zhou, X. Ma, Z. Yan, S. Arik, Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design, Neural Networks, 169 (2024), 733-743. https://doi.org/10.1016/j.neunet.2023.11.007

[43] S. Zhao, L. Zhao, S. Wen, L. Cheng, 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

[44] R. Zhang, H. Wang, J. H. Park, P. He, X. Xie, Event-triggered impulsive fault-tolerant control for memristor-based RDNNs with actuator faults, IEEE Trans. Neural Netw. Learn. Syst., 34 (2023), 2993-3004. https://doi.org/10.1109/TNNLS.2021.3110756

[45] L. Feng, D. Li, C. Zhang, Y. Yang, Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays, Electron. Res. Arch., 32 (2024), 17-40. https://doi.org/10.3934/era.2024002

[46] X. Han, Y. Yu, X. Wang, J. Cai, X. Feng, J. Wang, et al., Fault-tolerant bumpless transfer control for fuzzy switched delayed memristive neural networks subject to false data injection attacks, Chaos Solitons Fractals, 193 (2025), 116080. https://doi.org/10.1016/j.chaos.2025.116080

[47] Z. Yan, X. Huang, Y. Fan, J. Xia, H. Shen, Threshold-function-dependent quasi-synchronization of delayed memristive neural networks via hybrid event-triggered control, IEEE Trans. Syst. Man Cybern. Syst., 51 (2020), 6712-6722. https://doi.org/10.1109/TSMC.2020.2964605

[48] Y. Xin, Y. Wang, L. Mu, Z. Cheng, Stability criteria of delayed memristor-based neural networks via continuous-time model and interval matrix approach, IEEE Trans. Syst. Man Cybern. Syst., 53 (2022), 2716-2725. https://doi.org/10.1109/TSMC.2022.3218347

[49] 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

[50] M. Solak, O. Faydasicok, S. Arik, A general framework for robust stability analysis of neural networks with discrete time delays, Neural Networks, 162 (2023), 186-198. https://doi.org/10.1016/j.neunet.2023.02.040

[51] Y. Cui, P. Cheng, Exponential synchronization of stochastic time-delayed memristor-based neural networks via pinning impulsive control, Int. J. Control Autom. Syst., 22 (2024), 2283-2292. https://doi.org/10.1007/s12555-022-1090-8

[52] Q. Song, Q. Wu, Y. Liu, Stabilization of chaotic quaternion-valued neutral-type neural networks via sampled-data control with two-sided looped functional approach, Nonlinear Anal. Model. Control, 29 (2024), 1150-1166. https://doi.org/10.15388/namc.2024.29.37852

[53] L. He, X. Zhang, T. Jiang, C. Tang, Guaranteed performance control for delayed Markov jump neural networks with output quantization and data-injection attacks, Int. J. Mach. Learn. Cybern., 16 (2025), 173-188. https://doi.org/10.1007/s13042-024-02195-3

[54] A. Seuret, F. Gouaisbaut, Hierarchy of LMI conditions for the stability analysis of time-delay systems, Syst. Control Lett., 81 (2015), 1-7. https://doi.org/10.1016/j.sysconle.2015.03.007

[55] A. Seuret, K. Liu, F. Gouaisbaut, Generalized reciprocally convex combination lemmas and its application to time-delay systems, Automatica, 95 (2018), 488-493. https://doi.org/10.1016/j.automatica.2018.06.017

[56] Y. Wang, L. Xie, C. E. De Souza, Robust control of a class of uncertain nonlinear systems, Syst. Control Lett., 19 (1992), 139-149. https://doi.org/10.1016/0167-6911(92)90097-C

[57] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory , SIAM, Philadelphia, 1994. https://doi.org/10.1137/1.9781611970777

[58] J. Zhou, J. Dong, S. Xu, C. K. Ahn, Input-to-state stabilization for Markov jump systems with dynamic quantization and multimode injection attacks, IEEE Trans. Syst. Man Cybern. Syst., 54 (2024), 2517-2529. https://doi.org/10.1109/TSMC.2023.3344869

[59] Y. He, Q. Wang, L. Xie, C. Lin, Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Trans. Autom. Control, 52 (2007), 293-299. https://doi.org/10.1109/TAC.2006.887907

[60] K. Liu, A. Seuret, Y. Xia, Stability analysis of systems with time-varying delays via the second-order Bessel-Legendre inequality, Automatica, 76 (2017), 138-142. https://doi.org/10.1016/j.automatica.2016.11.001