An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach

Chao Yang; Juntao Wu; Zhengyang Qiao; Chao Yang; Juntao Wu; Zhengyang Qiao

doi:10.3934/era.2023123

Electronic Research Archive

2023, Volume 31, Issue 5: 2428-2446. doi: 10.3934/era.2023123

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An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach

1.
Department of Mathematics and Computer Science, Changsha University, Changsha 410002, China
2.
Department of Mathematics, National University of Defense Technology, Changsha 410073, China

Received: 24 October 2022 Revised: 21 February 2023 Accepted: 23 February 2023 Published: 01 March 2023

In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.
- fixed-time stabilization,
- memristor,
- nonlinear coupling,
- indefinite derivative
Citation: Chao Yang, Juntao Wu, Zhengyang Qiao. An improved fixed-time stabilization problem of delayed coupled memristor-based neural networks with pinning control and indefinite derivative approach[J]. Electronic Research Archive, 2023, 31(5): 2428-2446. doi: 10.3934/era.2023123

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Abstract

In this brief, we propose a class of generalized memristor-based neural networks with nonlinear coupling. Based on the set-valued mapping theory, novel Lyapunov indefinite derivative and Memristor theory, the coupled memristor-based neural networks (CMNNs) can achieve fixed-time stabilization (FTS) by designing a proper pinning controller, which randomly controls a small number of neuron nodes. Different from the traditional Lyapunov method, this paper uses the implementation method of indefinite derivative to deal with the non-autonomous neural network system with nonlinear coupling topology between different neurons. The system can obtain stabilization in a fixed time and requires fewer conditions. Moreover, the fixed stable setting time estimation of the system is given through a few conditions, which can eliminate the dependence on the initial value. Finally, we give two numerical examples to verify the correctness of our results.

References

[1]	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 doi: 10.1038/nature06932
[2]	J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. U.S.A., 79 (1982), 2554–2558. https://doi.org/10.1073/pnas.79.8.2554 doi: 10.1073/pnas.79.8.2554
[3]	J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. U.S.A., 81 (1984), 3088–3092. https://doi.org/10.1073/pnas.81.10.3088 doi: 10.1073/pnas.81.10.3088
[4]	Z. Guo, J. Wang, Z. Yan, Passivity and passification of memristor-based recurrent neural networks with time-varying delays, IEEE Trans. Neural Networks Learn. Syst., 25 (2014), 2099–2109. https://doi.org/10.1109/TNNLS.2014.2305440 doi: 10.1109/TNNLS.2014.2305440
[5]	J. Xu, C. Li, X. He, T. Huang, Recurrent neural network for solving model predictive control problem in application of four-tank benchmark, Neurocomputing, 190 (2016), 172–178. https://doi.org/10.1016/j.neucom.2016.01.020 doi: 10.1016/j.neucom.2016.01.020
[6]	W. Mulder, S. Bethard, M. Moens, A survey on the application of recurrent neural networks to statistical language modeling, Comput. Speech Lang., 30 (2015), 61–98. https://doi.org/10.1016/j.csl.2014.09.005 doi: 10.1016/j.csl.2014.09.005
[7]	P. Miao, Y. Shen, Y. Li, L. Bao, Finite-time recurrent neural networks for solving nonlinear optimization problems and their application, Neurocomputing, 177 (2016), 120–129. https://doi.org/10.1016/j.neucom.2015.11.014 doi: 10.1016/j.neucom.2015.11.014
[8]	Z. Cai, L. Huang, L. Zhang, New exponential synchronization criteria for time-varying delayed neural networks with discontinuous activations, Neural Networks, 65 (2015), 105–114. https://doi.org/10.1016/j.neunet.2015.02.001 doi: 10.1016/j.neunet.2015.02.001
[9]	L. Huang, J. Wang, X. Zhou, Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations, Nonlinear Anal. Real World Appl., 10 (2009), 1651–1661. https://doi.org/10.1016/j.nonrwa.2008.02.022 doi: 10.1016/j.nonrwa.2008.02.022
[10]	X. Li, J. Fang, H. Li, Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays, Neurocomputing, 267 (2017), 396–405. https://doi.org/10.1016/j.neucom.2017.06.049 doi: 10.1016/j.neucom.2017.06.049
[11]	C. Huang, J. Cao, Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system, Physica A, 473 (2017), 262–275. https://doi.org/10.1016/j.physa.2017.01.009 doi: 10.1016/j.physa.2017.01.009
[12]	S. Yang, Z. Guo, J. Wang, Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling, IEEE Trans. Syst. Man Cybern.: Syst., 45 (2015), 1077–1086. https://doi.org/10.1109/TSMC.2014.2388199 doi: 10.1109/TSMC.2014.2388199
[13]	Y. Hong, J. Huang, Y. Xu, On an output finite-time stabilization problem, IEEE Trans. Autom. Control, 2 (2001), 305–309. https://doi.org/10.1109/9.905699 doi: 10.1109/9.905699
[14]	F. Xiao, L. Wang, J. Chen, Y. Gao, Finite-time formation control for muti-agent systems, Automatica, 45 (2009), 2605–2611. https://doi.org/10.1016/j.automatica.2009.07.012 doi: 10.1016/j.automatica.2009.07.012
[15]	Z. Cai, L. Huang, Z. Wang, X. Pan, S. Liu, Periodicity and Multi-periodicity generated by impulses control in delayed Cohen-Grossberg-type neural networks with discontinuous activations, Neural Networks, 143 (2021), 230–245. https://doi.org/10.1016/j.neunet.2021.06.013 doi: 10.1016/j.neunet.2021.06.013
[16]	C. Aouiti, F. Miaadi, Finite-time stabilization of neutral hopfield neural networks with mixed delays, Neural Process. Lett., 48 (2018), 1645–1669. https://doi.org/10.1007/s11063-018-9791-y doi: 10.1007/s11063-018-9791-y
[17]	J. Gao, P. Zhu, A. Alsaedi, F. E. Alsaadi, T. Hayat, A new switching control for finite-time synchronization of memristor-based recurrent neural networks, Neural Networks, 86 (2017), 1–9. https://doi.org/10.1016/j.neunet.2016.10.008 doi: 10.1016/j.neunet.2016.10.008
[18]	Y. Hong, Finite-time stabilization and stabilizability of a class of controllable systems, Syst. Control Lett., 46 (2002), 231–236. https://doi.org/10.1016/S0167-6911(02)00119-6 doi: 10.1016/S0167-6911(02)00119-6
[19]	L. Wang, Y. Shen, G. Zhang, Finite-time stabilization and adaptive control of memristor-based delayed neural networks, IEEE Trans. Neural Networks Learn. Syst., 28 (2017), 2648–2659. https://doi.org/10.1109/TNNLS.2016.2598598 doi: 10.1109/TNNLS.2016.2598598
[20]	M. Tan, W. Tian, Finite-time stabilization and synchronization of complex dynamical networks with nonidentical nodes of different dimensions, Nonlinear Dyn., 79 (2015), 731–741. https://doi.org/10.1007/s11071-014-1699-0 doi: 10.1007/s11071-014-1699-0
[21]	A. Polyakov, D. Efimov, W. Perruquetti, Finite-time and fixed-time stabilization: Implicit Lyapunov function approach, Automatica, 51 (2015), 332–340. https://doi.org/10.1016/j.automatica.2014.10.082 doi: 10.1016/j.automatica.2014.10.082
[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 doi: 10.1109/TAC.2011.2179869
[23]	Z. Cai, L. Huang, Z. Wang, Novel fixed-time stability criteria for discontinuous nonautonomous systems: Lyapunov method with indefinite derivative, IEEE Trans. Cybern., 52 (2020), 4286–4299. https://doi.org/10.1109/TCYB.2020.3025754 doi: 10.1109/TCYB.2020.3025754
[24]	C. Yang, L. Huang, Z. Cai, Fixed-time synchronization of coupled memristor-based neural networks with time-varying delays, Neural Networks, 116 (2019), 101–109. https://doi.org/10.1016/j.neunet.2019.04.008 doi: 10.1016/j.neunet.2019.04.008
[25]	J. Cao, R. Li, Fixed-time synchronization of delayed memristor-based recurrent neural networks, Sci. China Inf. Sci., 60 (2017), 108–122.
[26]	C. Hu, J. Yu, Z. Chen, H. Jiang, T. Huang, Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks, Neural Networks, 89 (2017), 74–83. https://doi.org/10.1016/j.neunet.2017.02.001 doi: 10.1016/j.neunet.2017.02.001
[27]	X. Zhu, X. Yang, F. Alsaadi, T. Hayat, Fixed-time synchronization of coupled discontinuous neural networks with nonidentical perturbations, Neural Process. Lett., 48 (2018), 1161–1174. https://doi.org/10.1007/s11063-017-9770-8 doi: 10.1007/s11063-017-9770-8
[28]	S. Wen, T. Huang, Z. Zeng, Y. Chen, P. Li, Circuit design and exponential stabilization of memristive neural networks, Neural Networks, 63 (2015), 48–56. https://doi.org/10.1016/j.neunet.2014.10.011 doi: 10.1016/j.neunet.2014.10.011
[29]	J. Chen, Y. Wu, Y. Yang, S. Wen, K. Shi, A. Bermak, et al., An efficient Memristor-based circuit implementation of squeeze-and-excitation fully convolutional neural networks, IEEE Trans. Neural Networks Learn. Syst., 33 (2020), 1779–1790. https://doi.org/10.1109/TNNLS.2020.3044047 doi: 10.1109/TNNLS.2020.3044047
[30]	S. Wen, J. Chen, Y. Wu, Z. Yan, Y. Cao, Y. Yang, et al., CKFO: Convolution kernel first operated algorithm with applications in Memristor-based convolutional neural network, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 40 (2020), 1640–1647. https://doi.org/10.1109/TCAD.2020.3019993 doi: 10.1109/TCAD.2020.3019993
[31]	S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D. U. Hwang, Complex networks: structure and dynamics, Phys. Rep., 424 (2006), 175–308. https://doi.org/10.1016/j.physrep.2005.10.009 doi: 10.1016/j.physrep.2005.10.009
[32]	W. Lu, T. Chen, New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D, 213 (2006), 214–230. https://doi.org/10.1016/j.physd.2005.11.009 doi: 10.1016/j.physd.2005.11.009
[33]	J. Lv, X. Yu, G. Chen, Chaos synchronization of general complex dynamical networks, Physica A, 1334 (2004), 281–302. https://doi.org/10.1016/j.physa.2003.10.052 doi: 10.1016/j.physa.2003.10.052
[34]	H. Liu, B. Wang, J. Lu, Z. Li, Node-set importance and optimization algorithm of nodes selection in complex networks based on pinning control, Acta Phys. Sin., 70 (2021), 056401. https://doi.org/10.7498/aps.70.20200872 doi: 10.7498/aps.70.20200872
[35]	R. Rakkiyappan, B. Kaviarasan, F. Rihan, S. Lakshmanan, Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control, J. Franklin Inst., 352 (2015), 3178–3195. https://doi.org/10.1016/j.jfranklin.2014.12.017 doi: 10.1016/j.jfranklin.2014.12.017
[36]	P. Lin, W. Zhou, J. Fang, D. Li, A novel active pinning control for synchronization andanti-synchronization of new uncertain unified chaoticsystems, Nonlinear Dyn., 62 (2010), 417–425. https://doi.org/10.1007/s11071-010-9728-0 doi: 10.1007/s11071-010-9728-0
[37]	R. Vadivel, P. Hammachukiattikul, Q. Zhu, N. Gunasekaran, Event-triggered synchronization for stochastic delayed neural networks: passivity and passification case, Asian J. Control, (2022), 1–18. https://doi.org/10.1002/asjc.2965 doi: 10.1002/asjc.2965
[38]	R. Vadivel, R. Suresh, P. Hammachukiattikul, B. Unyong, N. Gunasekaran, Event-triggered $L_{2}$–$L_{\infty}$ filtering for network-based neutral systems with time-varying delays via T-S fuzzy approach, IEEE Access, 9 (2021), 145133–145147. https://doi.org/10.1109/ACCESS.2021.3123058 doi: 10.1109/ACCESS.2021.3123058
[39]	R. Vadivel, S. Sabarathinam, Y. Wu, K. Chaisena, N. Gunasekaran, New results on T-S fuzzy sampled-data stabilization for switched chaotic systems with its applications, Chaos, Solitons Fractals, 164 (2022), 112741. https://doi.org/10.1016/j.chaos.2022.112741 doi: 10.1016/j.chaos.2022.112741
[40]	H. Zhang, J. Cheng, H. Zhang, W. Zhang, J. Cao, Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays, Chaos, Solitons Fractals, 152 (2021), 111432. https://doi.org/10.1016/j.chaos.2021.111432 doi: 10.1016/j.chaos.2021.111432
[41]	H. Zhang, Y. Cheng, H. Zhang, W. Zhang, J. Cao, Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects, Math. Comput. Simul., 197 (2022), 341–357. https://doi.org/10.1016/j.matcom.2022.02.022 doi: 10.1016/j.matcom.2022.02.022
[42]	C. Wang, H. Zhang, I. Stamova, J. Cao, Global synchronization for BAM delayed reaction-diffusion neural networks with fractional partial differential operator, J. Franklin Inst., 360 (2023), 635–656. https://doi.org/10.1016/j.jfranklin.2022.08.038 doi: 10.1016/j.jfranklin.2022.08.038
[43]	T. Andy, Memristor-based neural networks, J. Phys. D: Appl. Phys., 46 (2013), 093001. https://doi.org/10.1088/0022-3727/46/9/093001 doi: 10.1088/0022-3727/46/9/093001
[44]	S. H. Strogatz, I. Stewart, Coupled oscillators and biological synchronization, Sci. Am., 6 (1993), 102–109. https://doi.org/10.1038/scientificamerican1293-102 doi: 10.1038/scientificamerican1293-102
[45]	J. P. Aubin, A. Cellina, Differential Inclusions, (1984), 8–13. https://doi.org/10.1007/978-3-642-69512-4
[46]	J. LaSalle, The Stability of Dynamical Systems, SIAM, 1976.
[47]	A. f. Filippov, Differential Equations with Discontinuous Righthand Sides: Control Systems, Springer Science & Business Media, 18 (2013).
[48]	F. H. Clarke, Optimization and Nonsmooth Analysis, SIAM, 1990. https://doi.org/10.1137/1.9781611971309
[49]	G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge University Press, London, 1952.

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