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Finite-Time and Fixed-Time Stabilization Control of Delayed Memristive Neural Networks: Robust Analysis Technique

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Abstract

This paper provides finite-time and fixed-time stabilization control strategy for delayed memristive neural networks. Considering that the parameters in the memristive model are state-dependent, which may contain unexpected parameter mismatch when different initial conditions are chosen, in this case, the traditional robust control and analytical methods cannot be carried out directly. To overcome this problem, a brand new robust control strategy was designed under the framework of Filippov solution. Based on the designed discontinuous controller, numerically testable conditions are proposed to stabilize the states of the target system in finite time and fixed time. Moreover, the upper bound of the settling time for stabilization is estimated. Finally, numerical examples are exhibited to explain our findings.

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References

  1. Chua L (1971) Memristor-the missing circut element. IEEE Trans Circuit Theory 18:507–519

    Article  Google Scholar 

  2. Strukov D, Snider G, Stewart D, Williams R (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  3. Wang F (2008) Commentary: memristor and memristive switch mechanism. J Nanophotonics 2:020304

    Article  Google Scholar 

  4. Snider G (2007) Self-organized computation with unreliable. Memrisitive nanodevices. Nanotechnology 18:365202

    Article  Google Scholar 

  5. Guo Z, Wang J, Yan Z (2013) Attractivity analysis of memristor-based cellular neural networks with time-varying delays. IEEE Trans Neural Netw Learn Syst 25:704–717

    Article  Google Scholar 

  6. Wang L, Shen Y, Sheng Y (2016) Finite-time robust stabilization of uncertain delayed neural networks with discontinuous activations via delayed feedback control. Neural Netw 76:46–54

    Article  Google Scholar 

  7. Muthukumar P, Subramanian K, Lakshmanan S (2016) Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays. J Franklin Inst 353:4091–4113

    Article  MathSciNet  MATH  Google Scholar 

  8. Ren F, Cao J (2006) LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal Real World Appl 7:967–979

    Article  MathSciNet  MATH  Google Scholar 

  9. Yan Z, Zhang G, Zhang W (2013) Finite time stability and stabilization of linear Itö stochastic systems with state and control dependent noise. Asian J Control 15:270–281

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu X, Ho WC, Daniel YuW, Cao J (2014) A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks. Neural Netw 57:94–102

    Article  MATH  Google Scholar 

  11. Bao H, Cao J (2012) Exponential stability for stochastic BAM networks with discrete and distributed delays. Appl Math Comput 218:6188–6199

    MathSciNet  MATH  Google Scholar 

  12. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23:1709–1726

    Article  MathSciNet  MATH  Google Scholar 

  13. Dorato P (1961) Short time stability in linear time-varying systems. In: Proceedings of the IRE international convention record part 4, New York, USA, pp 83–87

  14. Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57:2106–2110

    Article  MathSciNet  MATH  Google Scholar 

  15. Levant A (2013) On fixed and finite time stability in sliding mode control. In: Proceedings of 52nd IEEE conference on decision and control, Florence, Italy, pp 4260-4265

  16. Parsegv S, Polyakov A, Shcherbakov P (2013) Nonlinear fixed-time control protocol for uniform allocation of agents on a segment. In: Proceedings of 51nd IEEE conference on decision and control. IEEE, Maui, USA, pp 7732-7737

  17. Cao J, Li R (2017) Fixed-time synchronization of delayed memristor-based recurrent neural networks. Sci China Inf Sci 60:032201

    Article  Google Scholar 

  18. Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks. Neural Netw 73:86–94

    Article  Google Scholar 

  19. Zhang G, Shen Y, Xu C (2015) Global exponential stability in a Lagrange sense for memristive recurrent neural networks with time-varying delays. Neurocomputing 149:1330–1336

    Article  Google Scholar 

  20. Li R, Cao J (2016) Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. Appl Math Comput 278:54–69

    MathSciNet  Google Scholar 

  21. Wang Z, Ding S, Huang Z, Zhang H (2015) Exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method. IEEE Trans Neural Netw Learn Syst 129:2029–2035

    Google Scholar 

  22. Yang X, Cao J, Liang J (2017) Exponential synchronization of memristive neural networks with delays: interval matrix method. IEEE Trans Neural Netw Learn Syst 28:1878–1888

    Article  MathSciNet  Google Scholar 

  23. Li R, Wei H (2016) Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms via sampled data control. Int J Mach Learn Cybern 7:157–169

    Article  Google Scholar 

  24. Rakkiyappan R, Premalatha S, Chandrasekar A, Cao J (2016) Stability and synchronization analysis of inertial memristive neural networks with time delays. Cogn Neurodynamics 10:437–451

    Article  Google Scholar 

  25. Li R, Cao J (2016) Finite-time stability analysis for markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2016.2609148

    Google Scholar 

  26. Ding S, Wang Z (2015) Stochastic exponential synchronization control of memristive neural networks with multiple time-varying delays. Neurocomputing 162:16–25

    Article  Google Scholar 

  27. Wang L, Shen Y (2015) Finite-time stabilizability and instabilizability of delayed memristive neural networks with nonlinear discontinuous controller. IEEE Trans Neural Netw Learn Syst 26:2914–2924

    Article  MathSciNet  Google Scholar 

  28. Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys D Nonlinear Phenomena 214:88–99

    Article  MathSciNet  MATH  Google Scholar 

  29. Clarke F (1987) Optimization and nonsmooth analysis. SIAM, Philadelphia

    MATH  Google Scholar 

  30. Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence infinite time of delayed neural networks with infinite gain. IEEE Trans Neural Netw Learn Syst 16:1449–1463

    Article  Google Scholar 

  31. Parsegv S, Polyakov A, Shcherbakov P (2013) On fixed and finite time stability in sliding mode control. In: Proceedings of 4th IFAC workshop on distributed estimation and control in networked systems, Koblenz, Germany, pp 110–115

  32. Aubin JP, Cellina A (1984) Differential inclusions. Springer, Berlin

    Book  MATH  Google Scholar 

  33. Hardy G, Littlewood J, Polya G (1952) Inequalities, 2nd edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096, China

    Ruoxia Li & Jinde Cao

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jinde Cao

Authors
  1. Ruoxia Li
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  2. Jinde Cao
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Corresponding author

Correspondence to Jinde Cao.

Additional information

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 61573096 and 61272530, the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2012741, the “333 Engineering” Foundation of Jiangsu Province of China under Grant No. BRA2015286, the “Fundamental Research Funds for the Central Universities”, the JSPS Innovation Program under Grant KYZZ16_0115, and Scientific Research Foundation of Graduate School of Southeast University under Grant No. YBJJ1663.

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Li, R., Cao, J. Finite-Time and Fixed-Time Stabilization Control of Delayed Memristive Neural Networks: Robust Analysis Technique. Neural Process Lett 47, 1077–1096 (2018). https://doi.org/10.1007/s11063-017-9689-0

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  • DOI: https://doi.org/10.1007/s11063-017-9689-0

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