Abstract
This paper studies the problem of finite-time robust stabilization of inertial delayed neural networks with external disturbances. The finite-time stability research of inertial neural networks can be applied to important fields such as secure communication, so it has great significant research value. However, up to now, there are few previous studies on the finite-time stability of inertial neural networks, thus this paper makes up for this gap. Based on the actual communication networks, we improve the model of inertial neural networks, adding uncertainties and external disturbances. Unlike many previous papers based on scalar sign function, this paper introduces vector sign function, combines the constructed Lyapunov function, some inequality conditions, and related lemmas to design two effective controllers composed of \(U_1(t)\) and \(U_2(t)\), which can handle uncertainties and external disturbances of the neural networks well, and realize finite-time robust stability of the neural networks with external disturbances. In addition, the theoretical part of this paper estimates an upper bound on the settling time for the system to reach stability. Under the conditions of a certain strategy, we further optimize the extremes of the settling time so that the system reaches stability in a shorter time. Our results improve and extend some recent works. Finally, two examples are given to verify the validity and correctness of the designed controllers by numerical simulations using MATLAB tool.
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References
Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554–2558
Michel AN, Farrell JA, Sun H-F (1990) Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory. IEEE Trans Circuits Syst 37(11):1356–1366
Wang Z, Ding S, Shan Q, Zhang H (2017) Stability of recurrent neural networks with time-varying delay via flexible terminal method. IEEE Trans Neural Netw Learn Syst 28(10):2456–2463
Abd Elaziz M, Dahou A, Abualigah L et al (2021) Advanced metaheuristic optimization techniques in applications of deep neural networks: a review. Neural Comput Appl 33(21):14079–14099
Mehrabi M, Moayedi H (2021) Landslide susceptibility mapping using artificial neural network tuned by metaheuristic algorithms. Environ Earth Sci 80(24):1–20
Liu Qingshan, Wang Jun (2015) \(L_1\)-minimization algorithms for sparse signal reconstruction based on a projection neural network. IEEE Trans Neural Netw Learn Syst 27(3):698–707
Tu Z, Zhao Y, Ding N, Feng Y, Zhang W (2019) Stability analysis of quaternion-valued neural networks with both discrete and distributed delays. Appl Math Comput 343:342–353
Shen JC, Ma D, Gu ZH et al (2016) Darwin: a neuromorphic hardware co-processor based on spiking neural networks. Sci China Inf Sci 59:023401
Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60(3):032201
Jiang B, Lou J, Lu J et al (2021) Synchronization of chaotic neural networks: average-delay impulsive control. IEEE Trans Neural Netw Learn Syst
Babcock KL, Westervelt RM (1986) Stability and dynamics of simple electronic neural networks with added inertia. Physica D 23:464–469
Huang C, Liu B (2019) New studies on dynamic analysis of inertial neural networks involving non-reduced order method. Neurocomputing 325:283–287
Prakash M, Balasubramaniam P, Lakshmanan S (2016) Synchronization of Markovian jumping inertial neural networks and its applications in image encryption. Neural Netw 83:86–93
Wang J, Tian L (2017) Global Lagrange stability for inertial neural networks with mixed time-varying delays. Neurocomputing 235:140–146
Cui N, Jiang H, Hu C et al (2018) Global asymptotic and robust stability of inertial neural networks with proportional delays. Neurocomputing 272:326–333
Xiao Q, Huang Z, Zeng Z (2017) Passivity analysis for memristor-based inertial neural networks with discrete and distributed delays. IEEE Trans Syst Man Cybern Syst 49(2):375–385
Kong F, Zhu Q, Huang T (2020) New fixed-time stability lemmas and applications to the discontinuous fuzzy inertial neural networks. IEEE Trans Fuzzy Syst
Wang W, Chen W (2020) Mean-square exponential stability of stochastic inertial neural networks. Int J Control 1–7
Feng Y, Xiong X, Tang R et al (2018) Exponential synchronization of inertial neural networks with mixed delays via quantized pinning control. Neurocomputing 310:165–171
Jiang B, Lu J, Liu Y (2020) Exponential stability of delayed systems with average-delay impulses. SIAM J Control Optim 58(6):3763–3784
Long C, Zhang G, Zeng Z (2020) Novel results on finite-time stabilization of state-based switched chaotic inertial neural networks with distributed delays. Neural Netw 129:193–202
Xiao SP, Lian HH, Zeng HB et al (2017) Analysis on robust passivity of uncertain neural networks with time-varying delays via free-matrix-based integral inequality. Int J Control Autom Syst 15(5):2385–2394
Chen Z, Wang X, Zhong S et al (2017) Improved delay-dependent robust passivity criteria for uncertain neural networks with discrete and distributed delays. Chaos Solitons Fractals 103:23–32
Chanthorn P, Rajchakit G, Kaewmesri P et al (2020) A delay-dividing approach to robust stability of uncertain stochastic complex-valued hopfield delayed neural networks. Symmetry 12(5):683
Li X, Song S, Wu J (2019) Exponential stability of nonlinear systems with delayed impulses and applications. IEEE Trans Autom Control 64(10):4024–4034
Li X, Li P (2021) Stability of time-delay systems with impulsive control involving stabilizing delays. Automatica 124:109336
Chen L, Huang T, Machado JAT et al (2019) Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays. Neural Netw 118:289–299
Xu Y, Yu J, Li W et al (2021) Global asymptotic stability of fractional-order competitive neural networks with multiple time-varying-delay links. Appl Math Comput 389:125498
Chen J, Li C, Yang X (2018) Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects. J Frankl Inst 355(15):7595–7608
Yang X, Li X (2021) Finite-time stability of nonlinear impulsive systems with applications to neural networks. IEEE Trans Neural Netw Learn Syst
Yang X, Li X, Cao J (2018) Robust finite-time stability of singular nonlinear systems with interval time-varying delay. J Franklin Inst 355(3):1241–1258
Xu C, Li P (2019) On finite-time stability for fractional-order neural networks with proportional delays. Neural Process Lett 50(2):1241–1256
Hu J, Sui G, Du S et al (2017) Finite-time stability of uncertain nonlinear systems with time-varying delay. Math Probl Eng 2017
Zhang X, Li X, Cao J et al (2018) Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty. J Frankl Inst 355(13):5394–5413
Pratap A, Raja R, Cao J et al (2018) Further synchronization in finite time analysis for time-varying delayed fractional order memristive competitive neural networks with leakage delay. Neurocomputing 317:110–126
Vadivel R, Hammachukiattikul P, Rajchakit G et al (2021) Finite-time event-triggered approach for recurrent neural networks with leakage term and its application. Math Comput Simul 182:765–790
Rajchakit G, Sriraman R, Lim CP et al (2021) Synchronization in finite-time analysis of Clifford-valued neural networks with finite-time distributed delays. Mathematics 9(11):1163
Pratap A, Raja R, Alzabut J et al (2020) Finite-time Mittag-Leffler stability of fractional-order quaternion-valued memristive neural networks with impulses. Neural Process Lett 51(2):1485–1526
Saravanan S, Syed Ali M, Rajchakit G et al (2021) Finite-time stability analysis of switched genetic regulatory networks with time-varying delays via Wirtinger’s integral inequality. Complexity
Niamsup P, Ratchagit K, Phat VN (2015) Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks. Neurocomputing 160:281–286
Narayanan G, Ali MS, Alam MI et al (2021) Adaptive fuzzy feedback controller design for finite-time Mittag–Leffler synchronization of fractional-order quaternion-valued reaction-diffusion fuzzy molecular modeling of delayed neural networks. IEEE Access 9:130862–130883
Boonsatit N, Sriraman R, Rojsiraphisal T et al (2021) Finite-time synchronization of Clifford-valued neural networks with infinite distributed delays and impulses. IEEE Access 9:111050–111061
Gong S, Yang S, Guo Z et al (2018) Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller. Neural Netw 102:138–148
Lakshmanan S, Prakash M, Lim CP et al (2016) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans Neural Netw Learn Syst 29(1):195–207
Alimi AM, Aouiti C, Assali EA (2019) Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 332:29–43
Liu X, Ho DWC, Yu W et al (2014) A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks. Neural Netw 57:94–102
Cui N, Jiang H, Hu C et al (2018) Global asymptotic and robust stability of inertial neural networks with proportional delays. Neurocomputing 272:326–333
Liu M, Jiang H, Hu C (2017) Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control. J Frankl Inst 354(13):5374–5397
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Hong, N., Zhang, W., Zhou, Z. et al. Design of Controllers for Finite-Time Robust Stabilization of Inertial Delayed Neural Networks with External Disturbances. Neural Process Lett 55, 9387–9408 (2023). https://doi.org/10.1007/s11063-023-11206-3
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DOI: https://doi.org/10.1007/s11063-023-11206-3