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Neural Processing Letters

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11-10-2021

Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method

Authors: Sunny Singh, Umesh Kumar, Subir Das, F. Alsaadi, Jinde Cao

Published in: Neural Processing Letters | Issue 2/2022

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Abstract

This article is concerned with the fixed time synchronization for a class of Quaternion valued neural networks (QVNNs) with mixed time varying delays. Firstly, the QVNNs are separated into four equivalent real valued neural networks (RVNNs). Then, a novel suitable controller is designed to establish the fixed time synchronization of the QVNNs with the help of Lyapunov function. To give a glimpse, the finite time and fixed time stability definitions are proposed. Two different expressions of settling time are obtained by using two different lemmas. Finally, the validation of the theoretical results is shown through numerical simulation to a specific example.

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Shen D, Xu Y (2016) Iterative learning control for discrete-time stochastic systems with quantized information. IEEE/CAA J Autom Sin 3(1):59–67MathSciNetCrossRef

Zhao D, Wang Z, Chen Y, Wei G (2020) Proportional-integral observer design for multidelayed sensor-saturated recurrent neural networks: a dynamic event-triggered protocol. IEEE Trans Cybern 50(11):4619–4632CrossRef

Liu Y, Zheng Y, Lu J, Cao J, Rutkowski L (2019) Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans Neural Netw Learn Syst 31(3):1022–1035MathSciNetCrossRef

Miao J, Kou KI (2020) Quaternion-based bilinear factor matrix norm minimization for color image inpainting. IEEE Trans Signal Process 68:5617–5631MathSciNetCrossRef

Xia Z, Liu Y, Lu J, Cao J, Rutkowski L (2020) Penalty method for constrained distributed quaternion-variable optimization. IEEE Trans Cybern

Zhao Z, Wang Z, Zou L, Guo G (2018) Finite-time state estimation for delayed neural networks with redundant delayed channels. IEEE Trans Syst Man Cybern Syst

Ding D, Wang Z, Han QL (2019) Neural-network-based output-feedback control with stochastic communication protocols. Automatica 106:221–229MathSciNetMATHCrossRef

Jin J (2021) An improved finite time convergence recurrent neural network with application to time-varying linear complex matrix equation solution. Neural Process Lett 53(1):777–786CrossRef

Wang Z, Liu X (2019) Exponential stability of impulsive complex-valued neural networks with time delay. Math Comput Simul 156:143–157MathSciNetMATHCrossRef

10.

Rakkiyappan R, Sivaranjani R, Velmurugan G, Cao J (2016) Analysis of global O (t- \(\alpha \)) stability and global asymptotical periodicity for a class of fractional-order complex-valued neural networks with time varying delays. Neural Netw 77:51–69MATHCrossRef

11.

Wang JL, Wu HN, Huang T, Ren SY (2014) Passivity and synchronization of linearly coupled reaction–diffusion neural networks with adaptive coupling. IEEE Trans Cybern 45(9):1942–1952CrossRef

12.

Wen S, Zeng Z, Huang T, Zhang Y (2013) Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans Fuzzy Syst 22(6):1704–1713CrossRef

13.

Zeng D, Zhang R, Park JH, Zhong S, Cheng J, Wu GC (2021) Reliable stability and stabilizability for complex-valued memristive neural networks with actuator failures and aperiodic event-triggered sampled-data control. Nonlinear Anal Hybrid Syst 39:100977MathSciNetMATHCrossRef

14.

Took CC, Mandic DP (2008) The quaternion LMS algorithm for adaptive filtering of hypercomplex processes. IEEE Trans Signal Process 57(4):1316–1327MathSciNetMATHCrossRef

15.

Miron S, Le Bihan N, Mars JI (2006) Quaternion-MUSIC for vector-sensor array processing. IEEE Trans Signal Process 54(4):1218–1229MATHCrossRef

16.

Xia Y, Jahanchahi C, Mandic DP (2014) Quaternion-valued echo state networks. IEEE Trans Neural Netw Learn Syst 26(4):663–673MathSciNet

17.

Zou C, Kou KI, Wang Y (2016) Quaternion collaborative and sparse representation with application to color face recognition. IEEE Trans Image Process 25(7):3287–3302MathSciNetMATHCrossRef

18.

Isokawa T, Kusakabe T, Matsui N, Peper F (2003) Quaternion neural network and its application. In: International conference on knowledge-based and intelligent information and engineering systems, pp 318–324

19.

Qin S, Feng J, Song J, Wen X, Xu C (2016) A one-layer recurrent neural network for constrained complex-variable convex optimization. IEEE Trans Neural Netw Learn Syst 29(3):534–544MathSciNetCrossRef

20.

Sahoo A, Xu H, Jagannathan S (2015) Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans Neural Netw Learn Syst 27(3):497–509MathSciNetCrossRef

21.

Jiang BX, Liu Y, Kou KI, Wang Z (2020) Controllability and observability of linear quaternion-valued systems. Acta Math Sin Engl Ser 36(11):1299–1314MathSciNetMATHCrossRef

22.

Duan L, Fang X, Fu Y (2019) Global exponential synchronization of delayed fuzzy cellular neural networks with discontinuous activations. Int J Mach Learn Cybern 10(3):579–589CrossRef

23.

Yau HT, Hung TH, Hsieh CC (2012) Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption. Sensors 12(6):7468–7484CrossRef

24.

Diab A, Marque C, Karlsson B, Hassan M (2013) Comparison of methods for evaluating signal synchronization and direction: application to uterine EMG signals. In: 2013 2nd international conference on advances in biomedical engineering, pp 14–17

25.

Cagnan H, Duff EP, Brown P (2015) The relative phases of basal ganglia activities dynamically shape effective connectivity in Parkinson’s disease. Brain 138(6):1667–1678

26.

Zhang H, Wang XY (2017) Complex projective synchronization of complex-valued neural network with structure identification. J Franklin Inst 354(12):5011–5025MathSciNetMATHCrossRef

27.

Sun Y, Liu Y (2021) Adaptive synchronization control and parameters identification for chaotic fractional neural networks with time-varying delays. Neural Process Lett 1–17

28.

Li J, He C, Zhang W, Chen M (2017) Adaptive synchronization of delayed reaction–diffusion neural networks with unknown non-identical time-varying coupling strengths. Neurocomputing 219:144–153CrossRef

29.

Kumar R, Kumar U, Das S, Qiu J, Lu J (2021) Effects of heterogeneous impulses on synchronization of complex-valued neural networks with mixed time-varying delays. Inf Sci 551:228–244MathSciNetCrossRef

30.

Li Y, Yang Z, Dong Z (2017) Asymptotical synchronization of memristor-based neural networks with time-varying delays via adaptive control. In: 2017 36th Chinese control conference (CCC), pp 4012–4017

31.

Mishra AK, Das S, Yadav VK (2021) Finite-time synchronization of multi-scroll chaotic systems with sigmoid non-linearity and uncertain terms. Chin J Phys

32.

Chen C, Li L, Peng H, Yang Y, Li T (2017) Finite-time synchronization of memristor-based neural networks with mixed delays. Neurocomputing 235:83–89CrossRef

33.

Cai Z, Huang L, Zhu M, Wang D (2016) Finite-time stabilization control of memristor-based neural networks. Nonlinear Anal Hybrid Syst 20:37–54MathSciNetMATHCrossRef

34.

Liu M, Jiang H, Hu C (2016) Finite-time synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. Neurocomputing 194:1–9CrossRef

35.

Velmurugan G, Rakkiyappan R, Cao J (2016) Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Netw 73:36–46MATHCrossRef

36.

Wu H, Wang X, Liu X, Cao J (2020) Finite/fixed-time bipartite synchronization of coupled delayed neural networks under a unified discontinuous controller. Neural Process Lett 52(2):1359–1376CrossRef

37.

Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetMATHCrossRef

38.

Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83MATHCrossRef

39.

Ni J, Liu L, Liu C, Hu X, Li S (2016) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155

40.

Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossberg neural networks. Neural Netw 73:86–94MATHCrossRef

41.

Zhang Y, Deng S (2020) Fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects. Neural Process Lett 52(2):1263–1290CrossRef

42.

Gao F, Wu Y, Zhang Z, Liu Y (2019) Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application. Nonlinear Anal Hybrid Syst 31:56–68MathSciNetMATHCrossRef

43.

Jiang B, Hu Q, Friswell MI (2016) Fixed-time attitude control for rigid spacecraft with actuator saturation and faults. IEEE Trans Control Syst Technol 24(5):1892–1898CrossRef

44.

Yang X, Li C, Song Q, Chen J, Huang J (2018) Global Mittag–Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw 105:88–103MATHCrossRef

45.

Chen D, Zhang W, Cao J, Huang C (2020) Fixed time synchronization of delayed quaternion-valued memristor-based neural networks. Adv Differ Equ 1:1–16MathSciNetMATH

46.

Kumar U, Das S, Huang C, Cao J (2020) Fixed-time synchronization of quaternion-valued neural networks with time-varying delay. Proc R Soc A 476(2241):20200324MathSciNetMATHCrossRef

47.

Wei R, Cao J (2019) Fixed-time synchronization of quaternion-valued memristive neural networks with time delays. Neural Netw 113:1–10MATHCrossRef

48.

Ding D, You Z, Hu Y, Yang Z, Ding L (2020) Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks. Int J Mod Phys B 2150032

49.

Deng H, Bao H (2019) Fixed-time synchronization of quaternion-valued neural networks. Phys A Stati Mech Appl 527(121351)

50.

Li T, Luo Q, Sun C, Zhang B (2009) Exponential stability of recurrent neural networks with time-varying discrete and distributed delays. Nonlinear Anal Real World Appl 10(4):2581–2589MathSciNetMATHCrossRef

51.

Lakshmanan M, Senthilkumar DV (2011) Dynamics of nonlinear time-delay systems. Springer, BerlinMATHCrossRef

52.

Fiagbedzi YA, Pearson AE (1987) A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23(3):311–326MathSciNetMATHCrossRef

53.

Hale JK, Lunel SMV (2013) Introduction to functional differential equations. Springer, Berlin, p 99

54.

Cao J, Wang J (2004) Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Netw 17(3):379–390MATHCrossRef

55.

Chen C, Li L, Peng H, Yang Y, Mi L, Zhao H (2020) A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. Neural Netw 123:412–419MATHCrossRef

56.

Song Q, Chen X (2018) Multistability analysis of quaternion-valued neural networks with time delays. IEEE Trans Neural Netw Learn Syst 29(11):5430–5440MathSciNetCrossRef

57.

Chen X, Zhao Z, Song Q, Hu J (2017) Multistability of complex-valued neural networks with time-varying delays. Appl Math Comput 294:18–35MathSciNetMATH

58.

Li D, Ge SS, Lee TH (2020) Fixed-time-synchronized consensus control of multiagent systems. IEEE Trans Control Netw Syst 8(1):89–98MathSciNetCrossRef

Title: Synchronization of Quaternion Valued Neural Networks with Mixed Time Delays Using Lyapunov Function Method
Authors: Sunny Singh
Umesh Kumar
Subir Das
F. Alsaadi
Jinde Cao
Publication date: 11-10-2021
Publisher: Springer US
Published in: Neural Processing Letters / Issue 2/2022
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-021-10657-w

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