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\(H_{\infty }\) Estimation for Markovian Jump Neural Networks With Quantization, Transmission Delay and Packet Dropout

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Abstract

This paper is concerned with the problem of robust \(H_{\infty }\) estimation for a class of Markovian jump neural networks with norm-bounded parameter uncertainties, time-varying delay and limited communication capacity including signal transmission delay, measurement quantization and data packet dropout, which occur simultaneously in the same networked control system framework. Our objective is to design mode-dependent \(H_{\infty }\) filter in the network environment in order to ensure the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed \(H_{\infty }\) norm level for the limited communication capacity and for all admissible uncertainties. We use the delay system method to deal with signal transmission delay and data packet dropout, utilize the sector bound approach to handle measurement quantization. We also construct a comprehensive stochastic Lyapunov–Krasovskii functional to show the inherent mode-dependent state delays in the neural networks itself and the network-induced signal transmission delay. The free-weighting matrix technique and a set of strict linear matrix inequalities are employed to derive novel conditions for the desired mode-dependent \(H_{\infty }\) filter. A numerical example is provided to verify the effectiveness and usefulness of the obtained main results.

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References

  1. Arik S (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays. IEEE Trans Neural Netw 16(3):580–586

    Article  Google Scholar 

  2. Ahn CK (2013) State estimation for T-S fuzzy Hopfield neural networks via strict output passivation of the error system. Int J Gen Syst 42(5):503–518

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen Y, Zheng W (2012) Stochastic state estimation for neural networks with distributed delays and Markovian jump. Neural Netw 25(1):14–20

    Article  MATH  Google Scholar 

  4. Duan Q, Park JH, Wu Z (2014) Exponential state estimator design for discrete-time neural networks with discrete and distributed time-varying delays. Complexity 20(1):38–48

    Article  MathSciNet  Google Scholar 

  5. Huang H, Huang T, Chen X (2015) Exponential generalized \(H_{2}\) filtering of delayed static neural networks. Neural Process Lett 41(3):407–419

    Article  Google Scholar 

  6. Joya G, Atencia MA, Sandoval F (2002) Hopfield neural network for optimization: study of the different dynamic. Neurocomputing 43:219–237

    Article  MATH  Google Scholar 

  7. Arik S (2014) A new condition for robust stability of uncertain neural networks with time delays. Neurocomputing 128:476–482

    Article  Google Scholar 

  8. Cao J, Chen G, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybernet Part B 38(2):488–498

    Article  MathSciNet  Google Scholar 

  9. Li H, Gao H, Shi P (2010) New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans Neural Netw 21(11):1482–1487

    Google Scholar 

  10. Liu Y, Wang Z, Liu X (2012) State estimation for discrete-time neural networks with markov-mode-dependent lower and upper bounds on the distributed delays. Neural Process Lett 36(1):1–19

    Article  Google Scholar 

  11. Lu J, Cao J (2008) Adaptive synchronization of uncertain dynamical networks with delayed coupling. Nonlinear Dyn 53(1–2):107C115

    MathSciNet  Google Scholar 

  12. Lu J, Ho DWC (2010) Globally exponential synchronization and synchronizability for general dynamical networks. IEEE Trans Syst Man Cybern Part B 40(2):350–361

    Article  Google Scholar 

  13. Lu J, Kurths J, Cao J, Mahdavi N, Huang C (2012) Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans Neural Netw Learn Syst 23(2):285–292

    Article  Google Scholar 

  14. Lu J, Zhong J, Tang Y, Huang T, Cao J, Kurths J (2014) Synchronization in output-coupled temporal Boolean networks. Sci Rep 4:1–11. doi:10.1038/srep06292

    Google Scholar 

  15. Zhang B, Xu S, Zou Y (2008) Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays. Neurocomputing 72:321–330

    Article  Google Scholar 

  16. Zhou J, Wang Z, Wang Y, Kong Q (2013) Synchronization in complex dynamical networks with interval time-varying coupling delays. Nonlinear Dyn 72(1–2):377–388

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang Z, Ho DWC, Liu X (2005) State estimation for delayed neural networks. IEEE Trans Neural Netw 16(1):279–284

    Article  Google Scholar 

  18. Wang Z, Liu Y, Liu X (2009) State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw 22(1):41–48

    Article  MATH  Google Scholar 

  19. Bao H, Cao J (2011) Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay. Neural Netw 24(1):19–28

    Article  MATH  Google Scholar 

  20. He Y, Wang Q, Wu M, Lin C (2006) Delay-dependent state estimation for delayed neural networks. IEEE Trans Neural Netw 17(4):1077–1081

    Article  Google Scholar 

  21. Lakshmanan S, Mathiyalagan K, Park JH, Sakthivel R, Rihan FA (2014) Delay-dependent \(H_{\infty }\) state estimation of neural networks with mixed time-varying delays. Neurocomputing 129:392–400

    Article  Google Scholar 

  22. Lee TH, Park JH, Kwon OM, Lee SM (2013) Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw 46:99–108

    Article  MATH  Google Scholar 

  23. Liang J, Wang Z, Liu X (2009) State estimation for coupled uncertain stochastic networks with missing measurement and time-varying delays: the discretetime case. IEEE Trans Neural Netw 20(5):781–793

    Article  Google Scholar 

  24. Mou S, Gao H, Qiang W, Fei Z (2008) State estimation for discrete-time neural networks with time-varying delays. Neurocomputing 72(1–3):643–647

    Article  Google Scholar 

  25. Mao X, Yuan C (2006) Stochastic differential equations with Markovian switching. Imperial College Press, London

    Book  MATH  Google Scholar 

  26. Xia J, Sun C, Zhang B (2012) New robust control for uncertain stochastic Markovian jumping systems with mixed delays based on decoupling method. J Franklin Inst 349(3):741–769

    Article  MathSciNet  MATH  Google Scholar 

  27. Xia J, Sun C, Teng X, Zhang H (2014) Delay-segment-dependent robust stability for uncertain discrete stochastic Markovian jumping systems with interval time delay. Int J Syst Sci 45(3):271–282

    Article  MathSciNet  MATH  Google Scholar 

  28. Xu S, Chen T, Lam J (2003) Robust \(H_{\infty }\) filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans Autom Control 48(5):900–907

    Article  MathSciNet  Google Scholar 

  29. Xu S, Lam J, Mao X (2007) Delay-dependent \(H_{\infty }\) control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans Circ Syst Regul Pap 54(9):2070–2077

    Article  MathSciNet  Google Scholar 

  30. Zhang B, Zheng W, Xu S (2013) Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans Circ Syst Regul Pap 54(9):1250–1263

    Article  MathSciNet  Google Scholar 

  31. Zheng B, Yang G (2014) Sliding mode control for Markov jump linear uncertain systems with partly unknown transition rates. Int J Syst Sci 45(10):1999–2011

    Article  MathSciNet  MATH  Google Scholar 

  32. Tino P, Cernansky M, Benuskova L (2004) Markovian architectural bias of recurrent neural networks. IEEE Trans Neural Netw 15(1):6–15

    Article  Google Scholar 

  33. Zhu Q, Cao J, Hayat T, Alsaadi F (2015) Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms. Neural Process Lett 41(1):1–27

    Article  Google Scholar 

  34. Ma Q, Xu S, Zou Y, Lu J (2011) Stability of stochastic Markovian jump neural networks with mode-dependent delays. Neurocomputing 74:2157–2163

    Article  Google Scholar 

  35. SyedAli M, Marudaib M (2011) Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays. Math Comput Modell 54(9–10):1979–1988

    Article  MathSciNet  Google Scholar 

  36. Wu Z, Su H, Chu J (2010) State estimation for discrete Markovian jumping neural networks with time delay. Neurocomputing 73:2247–2254

    Article  Google Scholar 

  37. Xia J, Park JH, Zeng H (2015) Improved delay-dependent robust stability analysis for neutral-type uncertain neural networks with Markovian jumping parameters and time-varying delays. Neurocomputing 149:1198–1205

    Article  Google Scholar 

  38. Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19(2):366–370

    Article  Google Scholar 

  39. Balasubramaniam P, Lakshmanan S, Jeeva Sathya Theesar S (2010) State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn 60(4):661–675

    Article  MathSciNet  MATH  Google Scholar 

  40. Liu Y, Wang Z, Liu X (2008) State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. Phys Lett A 372(48):7147–7155

    Article  MathSciNet  MATH  Google Scholar 

  41. Gao H, Chen T (2007) \(H_{\infty }\) Estimation for uncertain systems with limited communication capacity. IEEE Trans Autom Control 52(11):2070–2084

    Article  MathSciNet  Google Scholar 

  42. Hu S, Yue D, Liu J (2012) \(H_{\infty }\) filtering for networked systems with partly known distribution transmission delays. Inform Sci 194:270–282

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang C, Feng G, Gao H, Qiu J (2011) \(H_{\infty }\) Filtering for nonlinear discrete-time systems subject to quantization and packet dropouts. IEEE Trans Fuzzy Syst 19(2):353–365

    Article  Google Scholar 

  44. Fu M, Xie L (2005) The sector bound approach to quantized feedback control. IEEE Trans Autom Control 50(11):1698–1711

    Article  MathSciNet  Google Scholar 

  45. Li L, Ho DWC, Lu J (2013) A unified approach to practical consensus with quantized data and time delay. IEEE Trans Circu Syst Regul Pap 60(10):2668–2678

    Article  MathSciNet  Google Scholar 

  46. Li L, Ho DWC, Xu S (2014) A distributed event-triggered scheme for discrete-time multi-agent consensus with communication delays. IET Control Theory Appl 8(10):830–837

    Article  MathSciNet  Google Scholar 

  47. Zheng B, Yang G (2014) Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control. Int J Robust Nonlinear Control 24(2):228–246

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank the reviewers and the editors for their detailed and valuable comments, which greatly improved the manuscript. This work was supported by the National Natural Science Foundation of China under Grant 61403178, 61403199; the Natural Science Foundation of Jiangsu Province under Grant BK20140770.

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Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, Shandong, People’s Republic of China

    Guangming Zhuang, Jianwei Xia & Huasheng Zhang

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China

    Guangming Zhuang & Qian Ma

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  1. Guangming Zhuang
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  2. Qian Ma
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Correspondence to Guangming Zhuang.

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Zhuang, G., Ma, Q., Xia, J. et al. \(H_{\infty }\) Estimation for Markovian Jump Neural Networks With Quantization, Transmission Delay and Packet Dropout. Neural Process Lett 44, 317–341 (2016). https://doi.org/10.1007/s11063-015-9460-3

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