Aperiodic Sampled-data Control for Exponential Synchronization of Chaotic Delayed Neural Networks with Exponentially Decaying Gain

Abstract

This paper studies the exponential synchronization of chaotic delayed neural networks (CDNNs) under aperiodic sampled-data control. First, an aperiodic sampled-data controller with exponentially decaying gain is designed to enlarge the maximum sampling period and the maximum allowable delay while still preserving the stability of the closed-loop system. Then, a novel time-dependent Lyapunov functional that consists of the information of the exponential decay rate η is elaborately designed to analyze the stability of the closed-loop system instead of using the common “change of coordinates” method.With the aid of Lyapunov theory and some inequality techniques, the sufficient conditions are established to guarantee the exponential synchronization of master-slave CDNNs. Based on matrix transformation, the equivalent conditions in LMI form are established to design the feedback gain. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller and the obtained synchronization criteria.

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References

  1. [1]

    G. W. Irwin, K. Warwick, and K. J. Hunt, Neural Network Applications in Control, Institution of Electrical Engineers, 1995.

    Google Scholar 

  2. [2]

    H. Zhang, Z. Wang, and D. Liu, “Global asymptotic stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 5, pp. 855–873, May 2008.

    Google Scholar 

  3. [3]

    F. W. Lewis, S. Jagannathan, and A. Yesildirak, Neural Network Control of Robot Manipulators and Nonlinear Systems, CRC Press, 1998.

    Google Scholar 

  4. [4]

    J. H. Park, T. H. Lee, Y. Liu, and J. Chen, Dynamic Systems with Time Delays: Stability and Control, Singapore, Springer-Nature, 2019.

    Google Scholar 

  5. [5]

    H. Shen, S. Huo, H. Yan, J. H. Park, and V. Sreeram, “Distributed dissipative state estimation for Markov jump genetic regulatory networks subject to round-robin scheduling,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 3, pp. 762–771, 2020.

    MathSciNet  Google Scholar 

  6. [6]

    J. Zhu and J. Sun, “Stability and exponential stability of complex-valued discrete linear systems with delay,” International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1030–1037, January 2018.

    Google Scholar 

  7. [7]

    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,” Applied Mathematics and Computation, vol. 354, pp. 115–127, August 2019.

    MathSciNet  MATH  Google Scholar 

  8. [8]

    H. Shen, T. Wang, J. Cao, G. Lu, Y. Song, and T. Huang, “Non-fragile dissipative synchronization for Markovian memristive neural networks: A gain-scheduled control scheme,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 6, pp. 1841–1853, June 2019.

    MathSciNet  Google Scholar 

  9. [9]

    R. Sakthivel, M. Sathishkumar, B. Kaviarasan, and S. M. Anthoni, “Synchronization and state estimation for stochastic complex networks with uncertain inner coupling,” Neurocomputing, vol. 238, pp. 44–55, January 2017.

    Google Scholar 

  10. [10]

    T. Jing, D. Zhang, J. Mei, and Y. Fan, “Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control,” Journal of the Franklin Institute, vol. 356, no. 10, pp. 5464–5484, July 2019.

    MathSciNet  MATH  Google Scholar 

  11. [11]

    S. Lin, Y. Huang and S. Ren, “Analysis and pinning control for passivity of coupled different dimensional neural networks,” Neurocomputing, vol. 321, pp. 187–200, December 2018.

    Google Scholar 

  12. [12]

    Y. Fan, X. Huang, Y. Li, J. Cao, and G. Chen, “Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: An interval matrix and matrix measure combined method,” IEEE Transactions on Systems, Man and Cybernetics: Systems, vol. 49, no. 11, pp. 2254–2265, November 2019.

    Google Scholar 

  13. [13]

    Z. Zhang, Y. He, M. Wu, and Q. Wang, “Exponential synchronization of neural networks with time-varying delays via dynamic intermittent output feedback control,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 3, pp. 612–622, March 2019.

    Google Scholar 

  14. [14]

    X. Wang, Z. Wang, Y. Fan, J. Xia, and H. Shen, “Enhanced global asymptotic stabilization criteria for delayed fractional complex-valued neural networks with parameter uncertainty,” International Journal of Control, Automation and Systems, vol. 17, no. 4, pp. 880–895, April 2019.

    Google Scholar 

  15. [15]

    J. Cao and J. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, vol. 16, no. 1, pp. 013133, March 2006.

    MathSciNet  MATH  Google Scholar 

  16. [16]

    G. Zhang, T. Wang, T. Li and S. Fei, “Exponential synchronization for delayed chaotic neural networks with nonlinear hybrid coupling,” Neurocomputing, vol. 85, pp. 53–61, May 2012.

    Google Scholar 

  17. [17]

    H. Zhang, T. Ma, G. Huang and Z. Wang, “Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 3, pp. 831–844, June 2010.

    Google Scholar 

  18. [18]

    J. Baillieul and P. J. Antsaklis, “Control and communication challenges in networked real-time systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 9–28, January 2007.

    Google Scholar 

  19. [19]

    J. H. Park, H. Shen, X. H. Chang, T. H. Lee, Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals, Springer, Cham, Switzerland, 2018.

    Google Scholar 

  20. [20]

    Y. Zhang and Q. Han, “Network-based synchronization of delayed neural networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 3, pp. 676–689, March 2013.

    MathSciNet  Google Scholar 

  21. [21]

    Q. Han, Y. Liu and F. Yang, “Optimal communication network-based H quantized control with packet dropouts for a class of discrete-time neural networks with distributed time delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 2, pp. 426–434, February 2016.

    Google Scholar 

  22. [22]

    X. H. Chang, R. Huang, and J. H. Park, “Robust guaranteed cost control under digital communication channels,” IEEE Transactions on Industrial Informatics, vol. 16, no. 1, pp. 319–327, January 2020.

    Google Scholar 

  23. [23]

    X. H. Chang, R. Huang, H. Q. Wang, and L. Liu, “Robust design strategy of quantized feedback control,” IEEE Transactions on Circuits and Systems II: Express Briefs, 2019. DOI: 10.1109/TCSII.2019.2922311

    Google Scholar 

  24. [24]

    Z. Yan, X. Huang, J. Xia, H. Shen, “Threshold-functiondependent quasi-synchronization of delayed memristive neural networks via hybrid event-triggered control,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020. DOI: 10.1109/TSMC.2020.2964605

    Google Scholar 

  25. [25]

    X. Wang, Z. Wang, Q. Song, H. Shen, and X. Huang, “A waiting-time-based event-triggered scheme for stabilization of complex-valued neural networks,” Neural Networks, vol. 121, pp. 329–338, January 2020.

    MATH  Google Scholar 

  26. [26]

    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, vol. 117, pp. 216–224, September 2019.

    MATH  Google Scholar 

  27. [27]

    T. Chen and B. A. Francis, Optimal Sampled-data Control Systems, Springer Science & Business Media, 2012.

    Google Scholar 

  28. [28]

    A. Seuret, “A novel stability analysis of linear systems under asynchronous samplings,” Automatica, vol. 48, no. 1, pp. 177–182, January 2012.

    MathSciNet  MATH  Google Scholar 

  29. [29]

    T. H. Lee, J. H. Park, S. M. Lee, and O. M. Kwon, “Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control,” International Journal of Control, vol. 86, no. 1, pp. 107–119, January 2013.

    MathSciNet  MATH  Google Scholar 

  30. [30]

    C. H. Lee, S. H. Lee, M. J. Park, and O. M. Kwon, “Stability and stabilization criteria for sampled-data control system via augmented Lyapunov-Krasovskii functionals,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2290–2302, October 2018.

    Google Scholar 

  31. [31]

    R. Sakthivel, M. Sathishkumar, Y. Ren, and O. M. Kwon, “Fault-tolerant sampled-data control of singular networked cascade control systems,” International Journal of Systems Science, vol. 48, no. 10, pp. 2079–2090, April 2017.

    MathSciNet  MATH  Google Scholar 

  32. [32]

    E. Fridman, “A refined input delay approach to sampleddata control,” Automatica, vol. 46, no. 2, pp. 421–427, February 2010.

    MathSciNet  MATH  Google Scholar 

  33. [33]

    T. Ahmed-Ali, E. Fridman, F. Giri, L. Burlion, and F. Lamnabhi-Lagarrigue, “Using exponential time-varying gains for sampled-data stabilization and estimation,” Automatica, vol. 67, pp. 244–251, May 2016.

    MathSciNet  MATH  Google Scholar 

  34. [34]

    S. Ding, Z. Wang, and H. Zhang, “Event-triggered stabilization of neural networks with time-varying switching gains and input saturation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 10, pp. 5045–5056, October 2018.

    MathSciNet  Google Scholar 

  35. [35]

    W. Chen, D. Wei, and X. Lu, “Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 3298–3312, September 2014.

    MathSciNet  MATH  Google Scholar 

  36. [36]

    Y. Liu and S. M. Lee, “Synchronization criteria of chaotic Lur’e systems with delayed feedback PD control,” Neurocomputing, vol. 189, no. 37, pp. 66–71, May 2015.

    Google Scholar 

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Correspondence to Xia Huang.

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Recommended by Associate Editor Mathiyalagan Kalidass under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China under Grants 61973199, 61573008, and the Taishan Scholar Project of Shandong Province of China.

Jikai Wang received his B.Eng. degree in information and electrical engineering from Shandong Jianzhu University, Jinan, China, in 2018. He is currently pursuing the M.Eng. degree with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China. His current research interests include neural networks, sampled-data control and switched systems.

Xia Huang received hher M.S. and Ph.D. degrees in applied mathematics from Southeast University, Nanjing, China, in 2004 and 2007, respectively. She has been a Professor with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China, since 2018. Her current research interests include neural networks, fractional-order nonlinear systems, and memristor-based circuits and systems.

Zhen Wang received his B.S. degree in mathematics from Ocean University of China, Qingdao, China in 2004 and the Ph.D. degree in the School of Automation, Nanjing University of Science and Technology, Nanjing, China in 2014. Since 2004, he has been with Shandong University of Science and Technology, Qingdao 266590, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include nonlinear control, neural networks, fractional order systems.

Jianwei Xia received his Ph.D. degree in control theory and control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 2007. He is a Professor with the School of Mathematics Science, Liaocheng University, Liaocheng, China. From 2010 to 2012, he was a Post-Doctoral Research Associate with the School of Automation, Southeast University, Nanjing. From 2013 to 2014, he was a Post-Doctoral Research Associate with the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea. His current research interests include robust control, stochastic systems, and neural networks.

Hao Shen received his Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. From February 2013 to March 2014, he was a Post-Doctoral Fellow with the Department of Electrical Engineering, Yeungnam University, Korea. Since 2011, he has been with Anhui University of Technology, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include stochastic hybrid systems, complex networks, fuzzy systems and control, nonlinear control.

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Wang, J., Huang, X., Wang, Z. et al. Aperiodic Sampled-data Control for Exponential Synchronization of Chaotic Delayed Neural Networks with Exponentially Decaying Gain. Int. J. Control Autom. Syst. 18, 2898–2906 (2020). https://doi.org/10.1007/s12555-019-0818-6

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Keywords

  • Aperiodic sampled-data control
  • chaotic delayed neural networks
  • exponential synchronization
  • timedependent Lyapunov functionals
  • time-varying gain