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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 |
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.
Keywords:
Time delay,
reaction diffusion,
neural networks,
fault-tolerant control,
anti-synchronization.
Mathematics Subject Classification:
Primary: 92B20, 34D06; Secondary: 34H10.
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
![]()
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Synchronization of stochastic chaotic neural networks with reaction-diffusion terms, Nonlinear Dynam., 67 (2012), 2183-2196.
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Self-synchronization in coupled salt-water oscillators, Phys. D, 115 (1998), 313-320.
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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.
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Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821-824.
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F. Ren and J. Cao,
Anti-synchronization of stochastic perturbed delayed chaotic neural networks, Neural Comput. Appl., 18 (2009), 515-521.
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I. Stamova, T. 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.
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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.
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| [27] |
W. Tai, Q. Teng, Y. Zhou, J. 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. Wang, L. Li, Y. 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).
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| [30] |
J. Xia, G. Chen and W. Sun,
Extended dissipative analysis of generalized Markovian switching neural networks with two delay components, Neurocomputing, 260 (2017), 275-283.
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| [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.
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Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control, Neural Process. Lett., 50 (2019), 2073-2086.
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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. |
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Y. Zhou, J. Xia, H. Shen, J. 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. |
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J. Zhou, S. Xu, H. 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.
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Non-fragile observer-based $H_{\infty}$ control for stochastic time-delay systems, Appl. Math. Comput., 291 (2016), 69-83.
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show all references
References:
| [1] |
A. Abdulle, Y. 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. Cao, R. Rakkiyappan, K. 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. Chang, R. 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. Fan, X. Huang, Y. Li, J. 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. Fan, X. Huang, H. 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. Hou, Y. 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. Huang, S.-Y. Ren, J. 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. Jiao, J. H. Park, G. Zong, Y. 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. Lee, C. P. Lim, S. 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. Li, M. 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. Liu, J. 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. Ma, S. Xu, Y. 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. Nakata, T. Miyata, N. 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. Ozcan, M. S. Ali, J. Yogambigai, Q. 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. Stamova, T. 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. Tai, Q. Teng, Y. Zhou, J. 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. Wang, L. Li, Y. 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. Xia, G. 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. Yucel, M. S. Ali, N. 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. Zhang, X. 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. Zhang, S. Yang, C. 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. Zhang, L. Yu, Q. 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. Zhou, Y. Wang, X. Zheng, Z. 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. Zhou, J. Xia, H. Shen, J. 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. Zhou, S. Xu, H. 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. Zhou, J. 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. Zhuang, Q. Ma, B. Zhang, S. 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 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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