April  2021, 14(4): 1569-1589. 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  April 2021 Early access  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 and Continuous Dynamical Systems - S, 2021, 14 (4) : 1569-1589. doi: 10.3934/dcdss.2020357
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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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. 

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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. 

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

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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