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SCIENCE CHINA Information Sciences, Volume 63 , Issue 11 : 212201(2020) https://doi.org/10.1007/s11432-019-2664-7

Variable-sampling-period dependent global stabilization of delayed memristive neural networks based on refined switching event-triggered control

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  • ReceivedJun 11, 2019
  • AcceptedSep 2, 2019
  • PublishedOct 9, 2020

Abstract

This paper studies the stabilization problem of delayed memristive neural networks under event-triggered control. A refined switching event-trigger scheme that switches between variable sampling and continuous event-trigger can be designed by introducing an exponential decay term into the threshold function. Compared with the existing mechanisms, the proposed scheme can enlarge the interval between two successively triggered events and therefore can reduce the amount of triggering times. By constructing a time-dependent and piecewise-defined Lyapunov functional, a less-conservative criterion can be derived to ensure global stability of the closed-loop system. Based on matrix decomposition, equivalent conditions in linear matrix inequalities form of the above stability criterion can be established for the co-design of both the trigger matrix and the feedback gain. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and the advantages of the refined switching event-trigger scheme.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61973199, 61473178, 61573008). We would thank anonymous reviewers for their valuable suggestions.


References

[1] Chua L. Memristor-The missing circuit element. IEEE Trans Circuit Theor, 1971, 18: 507-519 CrossRef Google Scholar

[2] Wang L, Shen Y. Design of controller on synchronization of memristor-based neural networks with time-varying delays. Neurocomputing, 2015, 147: 372-379 CrossRef Google Scholar

[3] Yang X, Ho D W C. Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach.. IEEE Trans Cybern, 2016, 46: 3377-3387 CrossRef PubMed Google Scholar

[4] Yang X, Cao J, Liang J. Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method.. IEEE Trans Neural Netw Learning Syst, 2017, 28: 1878-1888 CrossRef PubMed Google Scholar

[5] Fan Y, Huang X, Li Y. Aperiodically Intermittent Control for Quasi-Synchronization of Delayed Memristive Neural Networks: An Interval Matrix and Matrix Measure Combined Method. IEEE Trans Syst Man Cybern Syst, 2019, 49: 2254-2265 CrossRef Google Scholar

[6] Li N, Cao J. Lag Synchronization of Memristor-Based Coupled Neural Networks via ω-Measure.. IEEE Trans Neural Netw Learning Syst, 2016, 27: 686-697 CrossRef PubMed Google Scholar

[7] Liu H J, Wang Z D, Shen B. Event-Triggered $H_{\infty~}$ State Estimation for Delayed Stochastic Memristive Neural Networks With Missing Measurements: The Discrete Time Case.. IEEE Trans Neural Netw Learning Syst, 2018, 29: 3726-3737 CrossRef PubMed Google Scholar

[8] Cao J, Li R. Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci, 2017, 60: 032201 CrossRef Google Scholar

[9] Jia J, Huang X, Li Y. Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay.. IEEE Trans Neural Netw Learning Syst, 2019, : 1-13 CrossRef PubMed Google Scholar

[10] Choi H, Jung H, Lee J. An electrically modifiable synapse array of resistive switching memory. Nanotechnology, 2009, 20: 345201 CrossRef PubMed ADS Google Scholar

[11] Kim H, Sah M P, Yang C. Neural Synaptic Weighting With a Pulse-Based Memristor Circuit. IEEE Trans Circuits Syst I, 2012, 59: 148-158 CrossRef Google Scholar

[12] Xiaofeng Liao , Jeubang Yu . Robust stability for interval Hopfield neural networks with time delay.. IEEE Trans Neural Netw, 1998, 9: 1042-1045 CrossRef PubMed Google Scholar

[13] Ailong Wu , Zhigang Zeng . Exponential stabilization of memristive neural networks with time delays.. IEEE Trans Neural Netw Learning Syst, 2012, 23: 1919-1929 CrossRef PubMed Google Scholar

[14] Guo Z, Wang J, Yan Z. Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays.. Neural Networks, 2013, 48: 158-172 CrossRef PubMed Google Scholar

[15] Zhang G, Shen Y. Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control.. IEEE Trans Neural Netw Learning Syst, 2015, 26: 1431-1441 CrossRef PubMed Google Scholar

[16] Wen S, Huang T, Zeng Z. Circuit design and exponential stabilization of memristive neural networks.. Neural Networks, 2015, 63: 48-56 CrossRef PubMed Google Scholar

[17] Ding S, Wang Z, Rong N. Exponential Stabilization of Memristive Neural Networks via Saturating Sampled-Data Control.. IEEE Trans Cybern, 2017, 47: 3027-3039 CrossRef PubMed Google Scholar

[18] Zhang W, Branicky M S, Phillips S M. Stability of networked control systems. IEEE Control Syst, 2001, 21: 84-99 CrossRef Google Scholar

[19] Ge X, Yang F, Han Q L. Distributed networked control systems: A brief overview. Inf Sci, 2017, 380: 117-131 CrossRef Google Scholar

[20] Hespanha J P, Naghshtabrizi P, Xu Y. A Survey of Recent Results in Networked Control Systems. Proc IEEE, 2007, 95: 138-162 CrossRef Google Scholar

[21] Ogren P, Fiorelli E, Leonard N E. Cooperative Control of Mobile Sensor Networks: Adaptive Gradient Climbing in a Distributed Environment. IEEE Trans Automat Contr, 2004, 49: 1292-1302 CrossRef Google Scholar

[22] Walsh G C, Ye H. Scheduling of networked control systems. IEEE Control Syst, 2001, 21: 57-65 CrossRef Google Scholar

[23] Tabuada P. Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks. IEEE Trans Automat Contr, 2007, 52: 1680-1685 CrossRef Google Scholar

[24] Borgers D P, Heemels W P M H. Event-separation properties of event-triggered control systems. IEEE Trans Automat Contr, 2014, 59: 2644-2656 CrossRef Google Scholar

[25] Heemels W P M H, Donkers M C F, Teel A R. Periodic Event-Triggered Control for Linear Systems. IEEE Trans Automat Contr, 2013, 58: 847-861 CrossRef Google Scholar

[26] Zhang X M, Han Q L, Zhang B L. An Overview and Deep Investigation on Sampled-Data-Based Event-Triggered Control and Filtering for Networked Systems. IEEE Trans Ind Inf, 2017, 13: 4-16 CrossRef Google Scholar

[27] Lunze J, Lehmann D. A state-feedback approach to event-based control. Automatica, 2010, 46: 211-215 CrossRef Google Scholar

[28] Yue D, Tian E, Han Q L. A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems. IEEE Trans Automat Contr, 2013, 58: 475-481 CrossRef Google Scholar

[29] Wen S, Zeng Z, Chen M Z Q. Synchronization of Switched Neural Networks With Communication Delays via the Event-Triggered Control.. IEEE Trans Neural Netw Learning Syst, 2017, 28: 2334-2343 CrossRef PubMed Google Scholar

[30] Wang J, Chen M, Shen H. Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model. NOnlinear Dyn, 2017, 87: 2741-2753 CrossRef Google Scholar

[31] Shen B, Wang Z, Qiao H. Event-Triggered State Estimation for Discrete-Time Multidelayed Neural Networks With Stochastic Parameters and Incomplete Measurements.. IEEE Trans Neural Netw Learning Syst, 2017, 28: 1152-1163 CrossRef PubMed Google Scholar

[32] Duan G, Xiao F, Wang L. Hybrid event- and time-triggered control for double-integrator heterogeneous networks. Sci China Inf Sci, 2019, 62: 022203 CrossRef Google Scholar

[33] Selivanov A, Fridman E. A switching approach to event-triggered control. In: Proceedings of the 54th IEEE Conference on Decision and Control, Osaka, 2015. 5468--5473. Google Scholar

[34] Selivanov A, Fridman E. Event-triggered $H_{\infty~}$ control: a switching approach. IEEE Trans Automat Contr, 2016, 61: 3221-3226 CrossRef Google Scholar

[35] Fei Z, Guan C, Gao H. Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme.. IEEE Trans Neural Netw Learning Syst, 2018, 29: 2558-2567 CrossRef PubMed Google Scholar

[36] Fan Y, Huang X, Shen H. Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme.. Neural Networks, 2019, 117: 216-224 CrossRef PubMed Google Scholar

[37] Filippov A F. Differential Equations with Discontinuous Righthand Sides. Boston: Kluwer, 1988. Google Scholar

[38] Aubin J P, Cellina A. Differential Inclusions. Berlin: Springer, 1984. Google Scholar

[39] Fridman E. A refined input delay approach to sampled-data control. Automatica, 2010, 46: 421-427 CrossRef Google Scholar

[40] Suh Y S. Stability and stabilization of nonuniform sampling systems. Automatica, 2008, 44: 3222-3226 CrossRef Google Scholar

[41] Seuret A, Gouaisbaut F. Wirtinger-based integral inequality: Application to time-delay systems. Automatica, 2013, 49: 2860-2866 CrossRef Google Scholar

[42] Zhou J P, Park J H, Ma Q. Non-fragile observer-based $\mathcal{H}_{\infty~}$ control for stochastic time-delay systems. Appl Math Comput, 2016, 291: 69--83. Google Scholar

[43] Boyd S, El Ghaoui L, Feron E, et al. Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994. Google Scholar

  • Figure 1

    (Color online) The chaotic attractor of system (1) with initial conditions $(~-1.3,0.8)~^{\rm~T}$.

  • Table 1  

    Table 1Comparison of triggering times $t_{s}$ for RSETC and SETC schemes at $\tilde{h}_{k}~=~0.06$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    SETC [33-35] $\alpha~=0$, $\beta~=1$ $130$ $100$
    RSETC $\alpha~=0.01$, $\beta~=1$ $55$ $42$
    RSETC $\alpha~=0.1$, $\beta~=1$ $44$ $33$
  • Table 2  

    Table 2Comparison of triggering times $t_{s}$ for different $\beta$ at $\tilde{h}_{k}~=~0.06$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    RSETC $\alpha~=0.1$, $\beta~=5$ $127$ $100$
    RSETC $\alpha~=0.1$, $\beta~=2$ $93$ $73$
    RSETC $\alpha~=0.1$, $\beta~=1$ $44$ $34$
  • Table 3  

    Table 3Comparison of the triggering times $t_{s}$ between RSETC and SETC schemes at $\tilde{h}_{k}~=~0.014$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    SETC [33-35] $\alpha~=0,\beta=5$ $333$ $100$
    RSETC $\alpha~=0.001$, $\beta=5$ $235~$ $70~$
    RSETC $\alpha~=0.01$, $\beta=5$ $227~$ $68~$
  • Table 4  

    Table 4Comparison of triggering times $t_{s}$ for different $\beta$ at $\tilde{h}_{k}~=~0.014$

    Method Parameters $t_{s}$ $m_{s}$ (%)
    RSETC $\alpha~=0.01$, $\beta=7$ $290$ $100$
    RSETC $\alpha~=0.01$, $\beta=5$ $227~$ $78~$
    RSETC $\alpha~=0.01$, $\beta=3$ $170~$ $58~$

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