doi: 10.3934/dcdss.2020357

Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion

1. 

School of Computer Science and Technology, Anhui University of Technology, Ma'anshan 243032, China

2. 

Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 38541, Republic of Korea

3. 

College of Mathematics and Systems Science, Shandong University of Science & Technology, Qingdao 266590, China

* Corresponding author: Ju H. Park

Received  August 2019 Revised  December 2019 Published  May 2020

Fund Project: The first author is supported by Open Project of Anhui Province Key Laboratory of Special and Heavy Load Robot under Grant TZJQR005-2020 and the Excellent Youth Talent Support Program of Universities in Anhui Province under Grant GXYQZD2019021

This paper is concerned with the issue of fault-tolerant anti-synchro-nization control for chaotic switched neural networks with time delay and reaction-diffusion terms under the drive-response scheme, where the response system is assumed to be disturbed by stochastic noise. Both arbitrary switching signal and average dwell-time limited switching signal are taken into account. With the aid of the Lyapunov-Krasovskii functional approach and combining with the generalized Itô formula, sufficient conditions on the mean-square exponential stability for the anti-synchronization error system are presented. Then, by utilizing some decoupling methods, constructive design strategies on the desired fault-tolerant anti-synchronization controller are proposed. Finally, an example is given to demonstrate the effectiveness of our design strategies.

Citation: Jianping Zhou, Yamin Liu, Ju H. Park, Qingkai Kong, Zhen Wang. Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020357
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show all references

References:
[1]

A. AbdulleY. Bai and G. Vilmart, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, Discrete Contin. Dyn. Syst. Ser. S, 8 (2015), 91-118.  doi: 10.3934/dcdss.2015.8.91.  Google Scholar

[2]

C. K. Ahn, Adaptive $H_{\infty}$ anti-synchronization for time-delayed chaotic neural networks, Prog. Theoretical Phys., 122 (2009), 1391-1403.  doi: 10.1143/PTP.122.1391.  Google Scholar

[3]

J. CaoR. RakkiyappanK. Maheswari and A. Chandrasekar, Exponential $H_{\infty}$ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities, Sci. China Technol. Sci., 59 (2016), 387-402.  doi: 10.1007/s11431-016-6006-5.  Google Scholar

[4]

X. ChangR. Liu and J. H. Park, A further study on output feedback $H_{\infty}$ control for discrete-time systems, IEEE Trans. Circuits Systems II: Express Briefs, 67 (2020), 305-309.  doi: 10.1109/TCSII.2019.2904320.  Google Scholar

[5]

N. D. Cong and T. S. Doan, On integral separation of bounded linear random differential equations, Discrete Contin. Dyn. Syst. Ser. S, 9 (2016), 995-1007.  doi: 10.3934/dcdss.2016038.  Google Scholar

[6]

Y. FanX. HuangY. LiJ. Xia and G. Chen, Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: An interval matrix and matrix measure combined method, IEEE Trans. Systems Man Cybernetics: Systems, 49 (2019), 2254-2265.  doi: 10.1109/TSMC.2018.2850157.  Google Scholar

[7]

Y. FanX. HuangH. Shen and J. Cao, Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme, Neural Networks, 117 (2019), 216-224.  doi: 10.1016/j.neunet.2019.05.014.  Google Scholar

[8]

J. Fell and N. Axmacher, The role of phase synchronization in memory processes, Nature Rev. Neurosci., 12 (2011), 105-118.  doi: 10.1038/nrn2979.  Google Scholar

[9]

J. P. Hespanha and A. S. Morse, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999, 2655–2660. doi: 10.1109/CDC.1999.831330.  Google Scholar

[10]

J. HouY. Huang and S. Ren, Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms, Neurocomputing, 330 (2019), 78-93.  doi: 10.1016/j.neucom.2018.10.079.  Google Scholar

[11]

Y.-L. HuangS.-Y. RenJ. Wu and B.-B. Xu, Passivity and synchronization of switched coupled reaction-diffusion neural networks with non-delayed and delayed couplings, Int. J. Comput. Math., 96 (2019), 1702-1722.  doi: 10.1080/00207160.2018.1463437.  Google Scholar

[12]

T. JiaoJ. H. ParkG. ZongY. Zhao and Q. Du, On stability analysis of random impulsive and switching neural networks, Neurocomputing, 350 (2019), 146-154.  doi: 10.1016/j.neucom.2019.03.039.  Google Scholar

[13]

R. Konnur, Synchronization-based approach for estimating all model parameters of chaotic systems, Phys. Rev. E, 67 (2003), 1387-1396.  doi: 10.1103/PhysRevE.67.027204.  Google Scholar

[14]

T. H. LeeC. P. LimS. Nahavandi and J. H. Park, Network-based synchronization of T-S fuzzy chaotic systems with asynchronous samplings, J. Franklin Inst., 355 (2018), 5736-5758.  doi: 10.1016/j.jfranklin.2018.05.023.  Google Scholar

[15]

X. LiM. Bohner and C. K. Wang, Impulsive differential equations: Periodic solutions and applications, Automatica J. IFAC, 52 (2015), 173-178.  doi: 10.1016/j.automatica.2014.11.009.  Google Scholar

[16]

T. L. Liao and N. S. Huang, An observer-based approach for chaotic synchronization with applications to secure communications, IEEE Trans. Circuits Systems I: Fundamental Theory Appl., 46 (1999), 1144-1151.  doi: 10.1109/81.788817.  Google Scholar

[17]

Y. LiuJ. H. Park and F. Fang, Global exponential stability of delayed neural networks based on a new integral inequality, IEEE Trans. Systems Man Cybernetics: Systems, 49 (2019), 2318-2325.  doi: 10.1109/TSMC.2018.2815560.  Google Scholar

[18]

E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci., 20 (1963), 130-141.  doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.  Google Scholar

[19]

Q. MaS. XuY. Zou and G. Shi, Synchronization of stochastic chaotic neural networks with reaction-diffusion terms, Nonlinear Dynam., 67 (2012), 2183-2196.  doi: 10.1007/s11071-011-0138-8.  Google Scholar

[20]

X. Mao, Razumikhin-type theorems on exponential stability of stochastic functional differential equations, Stochastic Process. Appl., 65 (1996), 233-250.  doi: 10.1016/S0304-4149(96)00109-3.  Google Scholar

[21]

S. NakataT. MiyataN. Ojima and K. Yoshikawa, Self-synchronization in coupled salt-water oscillators, Phys. D, 115 (1998), 313-320.  doi: 10.1016/S0167-2789(97)00240-6.  Google Scholar

[22]

N. OzcanM. S. AliJ. YogambigaiQ. Zhu and S. Arik, Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction-diffusion terms via sampled-data control, J. Franklin Inst., 355 (2018), 1192-1216.  doi: 10.1016/j.jfranklin.2017.12.016.  Google Scholar

[23]

L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821-824.  doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[24]

F. Ren and J. Cao, Anti-synchronization of stochastic perturbed delayed chaotic neural networks, Neural Comput. Appl., 18 (2009), 515-521.  doi: 10.1007/s00521-009-0251-5.  Google Scholar

[25]

I. StamovaT. Stamov and X. Li, Global exponential stability of a class of impulsive cellular neural networks with supremums, Internat. J. Adapt. Control Signal Process., 28 (2014), 1227-1239.  doi: 10.1002/acs.2440.  Google Scholar

[26]

V. Sundarapandian and R. Karthikeyan, Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control, European J. Sci. Res., 64 (2011), 94-106.   Google Scholar

[27]

W. TaiQ. TengY. ZhouJ. Zhou and Z. Wang, Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control, Appl. Math. Comput., 354 (2019), 115-127.  doi: 10.1016/j.amc.2019.02.028.  Google Scholar

[28]

Z. WangL. LiY. Li and Z. Cheng, Stability and Hopf bifurcation of a three-neuron network with multiple discrete and distributed delays, Neural Process. Lett., 48 (2018), 1481-1502.  doi: 10.1007/s11063-017-9754-8.  Google Scholar

[29]

I. Wedekind and U. Parlitz, Synchronization and antisynchronization of chaotic power drop-outs and jump-ups of coupled semiconductor lasers, Phys. Rev. E, 66 (2002). doi: 10.1103/PhysRevE.66.026218.  Google Scholar

[30]

J. XiaG. Chen and W. Sun, Extended dissipative analysis of generalized Markovian switching neural networks with two delay components, Neurocomputing, 260 (2017), 275-283.  doi: 10.1016/j.neucom.2017.05.005.  Google Scholar

[31]

Z. Yan, X. Huang and J. Cao, Variable-sampling-period dependent global stabilization of delayed memristive neural networks via refined switching event-triggered control, SCIENCE CHINA Information Sciences, in progress. doi: 10.1007/s11432-019-2664-7.  Google Scholar

[32]

D. Ye and G. Yang, Adaptive fault-tolerant tracking control against actuator faults with application to flight control, IEEE Trans. Control Systems Tech, 14 (2006), 1088-1096.  doi: 10.1109/TCST.2006.883191.  Google Scholar

[33]

E. YucelM. S. AliN. Gunasekaran and S. Arik, Sampled-data filtering of Takagi–Sugeno fuzzy neural networks with interval time-varying delays, Fuzzy Sets and Systems, 316 (2017), 69-81.  doi: 10.1016/j.fss.2016.04.014.  Google Scholar

[34]

X. ZhangX. Lv and X. Li, Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control, Nonlinear Dynam., 90 (2017), 2199-2207.  doi: 10.1007/s11071-017-3795-4.  Google Scholar

[35]

W. ZhangS. YangC. Li and Z. Li, Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control, Neural Process. Lett., 50 (2019), 2073-2086.  doi: 10.1007/s11063-019-09985-9.  Google Scholar

[36]

D. ZhangL. YuQ. G. Wang and C. J. Ong, Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay, IEEE Trans. Neural Networks Learning Systems, 23 (2012), 827-834.  doi: 10.1109/TNNLS.2012.2186824.  Google Scholar

[37]

J. ZhouY. WangX. ZhengZ. Wang and H. Shen, Weighted $H_{\infty}$ consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies, Nonlinear Dyn., 96 (2019), 853-868.  doi: 10.1007/s11071-019-04826-9.  Google Scholar

[38]

Y. ZhouJ. XiaH. ShenJ. Zhou and Z. Wang, Extended dissipative learning of time-delay recurrent neural networks, J. Franklin Inst., 356 (2019), 8745-8769.  doi: 10.1016/j.jfranklin.2019.08.003.  Google Scholar

[39]

J. ZhouS. XuH. Shen and B. Zhang, Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions, Internat. J. Systems Sci., 44 (2013), 1494-1503.  doi: 10.1080/00207721.2012.659693.  Google Scholar

[40]

K. Zhou and P. P. Khargonekar, Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Systems Control Lett., 10 (1988), 17-20.  doi: 10.1016/0167-6911(88)90034-5.  Google Scholar

[41]

J. ZhouJ. H. Park and Q. Ma, Non-fragile observer-based $H_{\infty}$ control for stochastic time-delay systems, Appl. Math. Comput., 291 (2016), 69-83.  doi: 10.1016/j.amc.2016.06.024.  Google Scholar

[42]

G. ZhuangQ. MaB. ZhangS. Xu and J. Xia, Admissibility and stabilization of stochastic singular Markovian jump systems with time delays, Systems Control Lett., 114 (2018), 1-10.  doi: 10.1016/j.sysconle.2018.02.004.  Google Scholar

Figure 1.  ADT switching signal
Figure 2.  Phase plane plot of the drive system at $ x = 0.5 $
Figure 3.  State evolution of the unforced drive-response systems at $ x = 0.5 $
Figure 4.  State evolution of the unforced error system
Figure 5.  State evolution of the controlled drive-response systems at $ x = 0.5 $
Figure 6.  State evolution of the error system under control
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