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Robust state estimation for stochastic complex-valued neural networks with sampled-data

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Abstract

In this paper, the robust state estimation problem is investigated for the complex-valued neural networks involving parameter uncertainties, mixed time delays, as well as stochastic disturbances by resorting to the sampled-data information from the available output measurements. The parameter uncertainties are assumed to be norm-bounded and the stochastic disturbances are assumed to be Brownian motions, which could reflect much more realistic dynamical behaviors of the complex-valued network under a noisy environment. The purpose of the addressed problem is to design an estimator for the complex-valued network such that, for all admissible parameter uncertainties and sampled output measurements, the dynamics of the state estimation error system is assured to be globally asymptotically stable in the mean square. Matrix inequality approach, robust analysis tool, as well as stochastic analysis techniques are utilized together to derive several delay-dependent sufficient criteria guaranteeing the existence of the desired state estimator. Finally, simulation examples are illustrated to demonstrate the feasibility of the proposed estimation design schemes.

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References

  1. Tanaka G, Aihara K (2009) Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction. IEEE Trans Neural Netw 20(9):1463–1473

    Article  Google Scholar 

  2. Jankowski S, Lozowski A, Zurada J (1996) Complex-valued multistate neural associative memory. IEEE Trans Neural Netw 7(6):1491–1496

    Article  Google Scholar 

  3. Hirose A (2006) Complex-valued neural networks. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Li C, Liao X, Yu J (2002) Complex-valued recurrent neural network with IIR neural model: traning and applications. Circ Syst Signal Process 21(5):461–471

    Article  MATH  Google Scholar 

  5. Nitta T (2004) Orthogonality of decision boundaries in complex-valued neural networks. Neural Comput 16 (1):73–97

    Article  MATH  Google Scholar 

  6. Amin MF, Murase K (2009) Single-layered complex-valued neural network for real-valued classification problems. Neurocomputing 72(4-6):945–955

    Article  Google Scholar 

  7. Hirose A, Yoshida S (2013) Relationship between phase and amplitude generalization errors in complex- and real-valuedfeedforward neural networks. Neural Comput Appl 22(7-8):1357–1366

    Article  Google Scholar 

  8. Zhou W, Zurada JM (2009) Discrete-time recurrent neural networks with complex-valued linear threshold neurons. IEEE Trans Circ Syst II Exp Briefs 56(8):669–673

    Google Scholar 

  9. Xu X, Zhang J, Shi J (2014) Exponential stability of complex-valued neural networks with mixed delays. Neurocomputing 128:483–490

    Article  Google Scholar 

  10. Lee DL (2001) Relaxation of the stability condition of the complex-valued neural networks. IEEE Trans Neural Netw 12(5):1260–1262

    Article  Google Scholar 

  11. Huang Y, Zhang H, Wang Z (2014) Multistability of complex-valued recurrent neural networks with real-imaginary-type activation functions. Appl Math Comput 229:187–200

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang Z, Yu S (2016) Global asymptotic stability for a class of complex-valued Cohen-Grossberg neural networks with time delays. Neurocomputing 171:1158–1166

    Article  Google Scholar 

  13. Khajanchi S, Banerjee S (2014) Stability an bifurcation analysis of delay induced tumor immune interaction model. Appl Math Comput 248:652–671

    MathSciNet  MATH  Google Scholar 

  14. Xu W, Cao J, Xiao M (2015) A new framework for analysis on stability and bifurcation in a class of neural networks with discrete and distributed delays. IEEE Trans Cybern 45(10):2224–2236

    Article  Google Scholar 

  15. Zhou B, Song Q (2013) Boundedness and complete stability of complex-valued neural networks with time delay. IEEE Trans Neural Netw Learn Syst 24(8):1227–1238

    Article  Google Scholar 

  16. Li X, Rakkiyappan R, Velmurugan G (2015) Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays. Inform Sci 294:645–665

    Article  MathSciNet  MATH  Google Scholar 

  17. Song Q, Zhao Z, Liu Y (2015) Stability analysis of complex-valued neural networks with probabilistic time-varying delays. Neurocomputing 159:96–104

    Article  Google Scholar 

  18. Zhang Z, Lin C, Chen B (2014) Global stability criterion for delayed complex-valued recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(9):1704–1708

    Article  Google Scholar 

  19. Fang T, Sun J (2014) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 25(9):1709–1713

    Article  Google Scholar 

  20. Rakkiyappan R, Velmurugan G, Li X, O’Regan D (2016) Global dissipativity of memristor-based complex-valued neural networks with time-varying delays. Neural Comput Appl 27(3):629–649

    Article  Google Scholar 

  21. Hu J, Li N, Liu X, Zhang G (2013) Sampled-data state estimation for delayed neural networks with Markovian jumping parameters. Nonlinear Dyn 73(1-2):275–284

    Article  MathSciNet  MATH  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. Shu H, Zhang S, Shen B, Liu Y (2016) Unknown input and state estimation for linear discrete-time systems with missing measurements and correlated noises. Int J Gen Syst 45(5): 648–661

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  25. Li Q, Shen B, Liu Y, Alsaadi FE (2016) Event-triggered \(H_{\infty }\) state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing 174:912–920

    Article  Google Scholar 

  26. Zou L, Wang Z, Gao H, Liu X (2015) Event-triggered state estimation for complex networks with mixed time delays via sampled data information: The continuous-time case. IEEE Trans Cybern 45(12):2804–2815

    Article  Google Scholar 

  27. Ding D, Wang Z, Shen B, Dong H (2015) Event-triggered distributed \(H_{\infty }\) state estimation with packet dropouts through sensor networks. IET Control Theory Appl 9(13):1948–1955

    Article  MathSciNet  Google Scholar 

  28. Ahn CK (2012) Switched exponential state estimation of neural networks based on passivity theory. Nonlinear Dyn 67(1):573–586

    Article  MathSciNet  MATH  Google Scholar 

  29. Liang J, Lam J, Wang Z (2009) State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates. Phys Lett A 373(47):4328–4337

    Article  MathSciNet  MATH  Google Scholar 

  30. Li N, Hu J, Hu J, Li L (2012) Exponential state estimation for delayed recurrent neural networks with sampled-data. Nonlinear Dyn 69:555–564

    Article  MathSciNet  MATH  Google Scholar 

  31. Anbuvithya R, Mathiyalagan K, Sakthivel R, Prakash P (2015) Sampled-data state estimation for genetic regulatory networks with time-varying delays. Neurocomputing 151:737–744

    Article  Google Scholar 

  32. Qiu B, Liao X, Zhou B (2015) State estimation for complex-valued neural networks with time-varying delays. In: Proceedings of Sixth International Conference on Intelligent Control and Information Processing, Wuhan, pp. 531–536

  33. Yang S, Guo Z, Wang J (2015) Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling. IEEE Trans Syst Man Cybern Syst 45(7):1077–1086

    Article  Google Scholar 

  34. Yao D, Lu Q, Wu C, Chen Z (2015) Robust finite-time state estimation of uncertain neural networks with Markovian jump parameters. Neurocomputing 159:257–262

    Article  Google Scholar 

  35. Huang H, Feng G, Cao J (2008) Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans Neural Netw 19(8):1329–1339

    Article  Google Scholar 

  36. Yang D, Liu X, Xu Y, Wang Y, Liu Z (2013) State estimation of recurrent neural networks with interval time-varying delay: an improved delay-dependent approach. Neural Comput Appl 23(3-4):1149–1158

    Article  Google Scholar 

  37. Liang J, Wang Z, Liu X (2014) Robust state estimation for two-dimensional stochastic time-delay systems with missing measurements and sensor saturation. Multidim Syst Signal Process 25(1):157–177

    Article  MATH  Google Scholar 

  38. Shen B, Wang Z, Huang T (2016) Stabilization for sampled-data systems under noisy sampling interval. Automatica 63:162–166

    Article  MathSciNet  MATH  Google Scholar 

  39. Boyd S, El Ghaoui L, Feyon E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM , Philadelphia

    Book  Google Scholar 

  40. Xie L (1996) Output feedback \(H_{\infty }\) control of systems with parameter uncertainty. Int J Control 63:741–750

    Article  MathSciNet  MATH  Google Scholar 

  41. Friedman A (1976) Stochastic differential equations and their applications. Academic Press, New York

    MATH  Google Scholar 

  42. Schuss Z (1980) Theory and applications of stochastic differential equations. Wiley, New York

    MATH  Google Scholar 

  43. Li X, Su H, Chen M (2016) Consensus networks with time-delays over finite fields. Int J Control 89 (5):1000–1008

    Article  MathSciNet  MATH  Google Scholar 

  44. Chen H, Liang J, Wang Z (2016) Pinning controllability of autonomous Boolean control networks. Sci China-Inf Sci 59(7):070107

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under Grant 61673110 and 61403248, the Six Talent Peaks Project for the High Level Personnel from the Jiangsu Province of China under Grant 2015-DZXX-003, the Fundamental Research Funds for the Central Universities under Grant 2242015K42009, the Shanghai Yangfan Program of China under Grant 14YF1409800, the Shanghai Young Teacher’s Training Program under Grant ZZgcd14005, the Zhanchi Program of Shanghai University of Engineering Science under Grant nhrc201514.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Weiqiang Gong & Jinling Liang

  2. School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, People’s Republic of China

    Xiu Kan

  3. Department of Fundamental Courses, Wuxi Institute of Technology, Wuxi, 214121, People’s Republic of China

    Lan Wang

  4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Abdullah M. Dobaie

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  1. Weiqiang Gong
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  2. Jinling Liang
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  3. Xiu Kan
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  4. Lan Wang
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  5. Abdullah M. Dobaie
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Correspondence to Jinling Liang.

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Gong, W., Liang, J., Kan, X. et al. Robust state estimation for stochastic complex-valued neural networks with sampled-data. Neural Comput & Applic 31 (Suppl 1), 523–542 (2019). https://doi.org/10.1007/s00521-017-3030-8

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  • DOI: https://doi.org/10.1007/s00521-017-3030-8

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