Advertisement

Finite-time Asynchronous H Filtering Design of Markovian Jump Systems with Randomly Occurred Quantization

  • Yangchen Zhu
  • Xiaona SongEmail author
  • Mi Wang
  • Junwei Lu
Article
  • 1 Downloads

Abstract

In this paper, the problem of asynchronous H filtering is discussed for discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems (FMJSs) with randomly occurred quantization. The asynchrony refers to the situation that the plant state and the filter state belong to different local state space regions, and the randomly occurred quantization is introduced to describe the quantisation phenomenon appearing in a probabilistic way. The aim of this study is to design an asynchronous H filter for discrete-time T-S FMJSs such that the resulting filtering error system satisfies H disturbance attention performance and finite-time boundedness. Then, the gains of the filter are obtained by solving a set of linear matrix inequalities. Finally, three examples are utilized to illustrate the effectiveness of our proposed approach.

Keywords

Asynchronous H filtering finite-time Markov jump systems randomly occurred quantization T-S fuzzy model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. [1]
    M. Zhang, P. Shi, L. Ma, J. Cai, and H. Su, “Quantized feedback control of fuzzy Markov jump systems,” IEEE Transactions on Cybernetics, vol. 49, no. 9, pp. 3375–3384, June 2018.CrossRefGoogle Scholar
  2. [2]
    M. Zhang, P. Shi, L. Ma, J. Cai, and H. Su, “Network-based fuzzy control for nonlinear Markov jump systems subject to quantization and dropout compensation,” Fuzzy Sets and Systems, vol. 371, pp. 96–109, September 2019.MathSciNetCrossRefGoogle Scholar
  3. [3]
    J. H. Park, H. Shen, X. Chang, and T. H. Lee, Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals, Springer, Cham, Switzerland, 2018.Google Scholar
  4. [4]
    X. Song, M. Wang, and S. Song, “Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links,” Applied Mathematics and Computation, vol. 353, no. 15, pp. 371–395, July 2019.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Z. Wu, P. Shi, Z. Shu, H. Su, and R. Lu, “Passivity-based asynchronous control for Markov jump systems,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 2020–2025, April 2017.MathSciNetCrossRefGoogle Scholar
  6. [6]
    X. Song, Y. Men, and J. Zhou, “Event-triggered H control for networked discrete-time Markov jump systems with repeated scalar nonlinearities,” Applied Mathematics and Computation, vol. 298, pp. 123–132, April 2017.MathSciNetCrossRefGoogle Scholar
  7. [7]
    H. Shen, F. Li, H. Yan, and H. K. Lam, “Finite-time event-triggered H control for T-S fuzzy Markov jump systems,” IEEE Transactions on Fuzzy Systems, vol. 26, pp. 3122–3135, January 2018.CrossRefGoogle Scholar
  8. [8]
    N. H. A. Nguyen and S. H. Kim, “Relaxed robust stabilization conditions for nonhomogeneous Markovian jump systems with actuator saturation and general switching policies,” International Journal of Control Automation and Systems, vol. 17, no. 3, pp. 586–596, March 2019.CrossRefGoogle Scholar
  9. [9]
    S. Dong, Z. Wu, P. Shi, H. R. Karimi, and H. Su, “Networked fault detection for Markov jump nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 6, pp. 3368–3378, April 2018.CrossRefGoogle Scholar
  10. [10]
    M. Hua, Z. Zhang, F. Yao, J. Ni, W. Dai, and Y. Cheng, “Robust H filtering for continuous-time nonhomogeneous Markov jump nonlinear systems with randomly occurring uncertainties,” Signal Processing, vol. 148, no. 5, pp. 18–27, July 2018.Google Scholar
  11. [11]
    T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116–132, January 1985.CrossRefGoogle Scholar
  12. [12]
    S. Song, B. Zhang, X. Song, and Z. Zhang, “Neuro-fuzzy-based adaptive dynamic surface control for fractional-order nonlinear strict-feedback systems with input constraint,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, August 2019. DOI: 10.1109/TSMC.2019.2933359Google Scholar
  13. [13]
    S. Dong, Z. Wu, Y. Pan, H. Su, and Y. liu, “Hidden-Markov-model-based asynchronous filter design of nonlinear Markov jump systems in continuous-time domain,” IEEE Transactions on Cybernetics, vol. 49, no. 6, pp. 2294–2304, May 2018.CrossRefGoogle Scholar
  14. [14]
    J. Cheng, B. Wang, and J. H. Park, “Sampled-data reliable control for T-S fuzzy semi-Markovian jump system and its application to single-link robot arm mode,” IET Control Theory and Applications, vol. 11, no. 12, pp. 1904–1912, May 2017.MathSciNetCrossRefGoogle Scholar
  15. [15]
    L. Monache, T. Nipen, Y. Liu, G. Roux, and R. Stull, “Kalman filter and analog schemes to postprocess numerical weather predictions” Monthly Weather Review, vol. 139, no. 11, pp. 3554–3570, November 2011.CrossRefGoogle Scholar
  16. [16]
    W. Wu, X. Ma, and X. Xu, “Application research on data segment by Robust H filter estimation” Proc. of Chinese Control and Decision Conference, pp. 680–683, June 2009.Google Scholar
  17. [17]
    K. Arakawa, “Median filter based on fuzzy rules and its application to image restoration,” Fuzzy Sets and Systems, vol. 77, no. 1, pp. 3–13, January 1996.CrossRefGoogle Scholar
  18. [18]
    M. Zhang, C. Shen, Z. Wu, and D. Zhang, “Dissipative filtering for switched fuzzy systems with missing measurements,” IEEE Transactions on Cybernetics, April 2019. DOI: 10.1109/TCYB.2019.2908430Google Scholar
  19. [19]
    T. Yang, L. Zhang, V. Sreeram, A. N. Vargas, T. Hayat, and B. Ahmad, “Time-varying filter design for semi-Markov jump linear systems with intermittent transmission,” International Journal of Robust and Nonlinear Control, vol. 27, no. 17, pp. 4035–4049, November 2017.MathSciNetzbMATHGoogle Scholar
  20. [20]
    Z. Yan, J. H. Park, and W. Zhang, “Quantitative exponential stability and stabilization of discrete-time Markov jump systems with multiplicative noises,” IET Control Theory and Applications, vol. 11, no. 16, pp. 2886–2892, August 2017.MathSciNetCrossRefGoogle Scholar
  21. [21]
    S. Dong, Z. Wu, P. Shi, H. Su, and T. Huang, “Quantized control of Markov jump nonlinear systems based on fuzzy hidden Markov model,” IEEE Transactions on Cybernetics, vol. 49, no. 7, pp. 2420–2430, March 2018.CrossRefGoogle Scholar
  22. [22]
    X. Bu, Y. Qiao, Z. Hou, and J. Yang, “Model free adaptive control for a class of nonlinear systems using quantized information,” Asian Journal of Control, vol. 20, no. 2, pp. 962–968, March 2018.MathSciNetCrossRefGoogle Scholar
  23. [23]
    X. Chang and Y. Wang, “Peak-to-peak filtering for networked nonlinear DC motor systems with quantization,” IEEE Transactions on Industrial Informatics, vol. 14, no. 12, pp. 5378–5388, December 2018.CrossRefGoogle Scholar
  24. [24]
    Q. Li, B. Shen, Z. Wang, and F. E. Alsaadi, “Event-triggered H state estimation for state-saturated complex networks subject to quantization effects and distributed delays,” Journal of the Franklin Institute, vol. 355, no. 5, pp. 2874–2891, March 2018.MathSciNetCrossRefGoogle Scholar
  25. [25]
    J. Tao, R. Lu, H. Su, P. Shi, and Z. Wu, “Asynchronous filtering of nonlinear Markov jump systems with randomly occurred quantization via T-S fuzzy models,” IEEE Transactions on Fuzzy systems, vol. 26, no. 4, pp. 1866–1877, September 2017.Google Scholar
  26. [26]
    C. Xu, X. Yang, J. Lu, J. Feng, F. E. Alsaadi, and T. Hayat, “Finite-time synchronization of networks via quantized intermittent pinning control,” IEEE Transactions on Cybernetics, vol. 48, no. 10, pp. 3021–3027, September 2017.CrossRefGoogle Scholar
  27. [27]
    Z. Cao, Y. Niu, and H. Zhao, “Finite-time sliding mode control of Markovian jump systems subject to actuator faults,” International Journal of Control, Automation and Systems, vol. 16, no. 5, pp. 2282–2289, September 2018.CrossRefGoogle Scholar
  28. [28]
    S. Song, B. Zhang, J. Xia, and Z. Zhang, “Adaptive backstepping hybrid fuzzy sliding mode control for uncertain fractional-order nonlinear systems based on finite-time scheme,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, December 2018. DOI:10.1109/TSMC.2018.2877042Google Scholar
  29. [29]
    X. Song, M. Wang, S. Song, and J. Lu, “Eventtriggered reliable H control for a class of nonlinear distributed parameter systems within a finite-time interval,” Journal of the Franklin Institute, July 2019. DOI: 10.1016/j.jfranklin.2019.06.027Google Scholar
  30. [30]
    D. F. Anderson, D. Cappelletti, and T. G. Kurtz, “Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness,” SIAM Journal on Applied Dynamical Systems, vol. 16, no. 3, pp. 1309–1339, July 2017.MathSciNetCrossRefGoogle Scholar
  31. [31]
    S. He, L. Kun, X. Huang, W. Zheng, and F. Liu, “Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities,” Applied Mathematical Modelling, vol. 35, no. 6, pp. 2631–2638, July 2011.MathSciNetCrossRefGoogle Scholar
  32. [32]
    J. Cheng, H. Zhu, Y. Ding, S. Zhong, and Q. Zhong, “Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 242, pp. 281–295, September 2014.MathSciNetCrossRefGoogle Scholar
  33. [33]
    J. Wang, F. Li, Y. Sun, and H. Shen, “On asynchronous l 2-l filtering for networked fuzzy systems with Markov jump parameters over a finite-time interval,” IET Control Theory & Applications, vol. 10, no. 17, pp. 2175–2185, November 2016.MathSciNetCrossRefGoogle Scholar
  34. [34]
    J. Song, Y. Niu, and Y. Zou, “Asynchronous output feedback control of time-varying Markovian jump systems within a finite-time interval,” Journal of the Franklin Institute, vol. 354, no. 15, pp. 6747–6765, October 2017.MathSciNetCrossRefGoogle Scholar
  35. [35]
    M. Zhang, P. Shi, Z. Liu, H. Su, and L. Ma, “Fuzzy model-based asynchronous H filter design of discrete-time Markov jump systems,” Journal of the Franklin Institute, vol. 354, no. 18, pp. 8444–8460, December 2017.MathSciNetCrossRefGoogle Scholar
  36. [36]
    X. Song, M. Wang, S. Song, and I. Tejado, “Reliable L 2L state estimation for Markovian jump reaction-diffusion neural networks with sensor saturation and asynchronous failure,” IEEE Access, vol. 6, pp. 50066–50076, Augest 2018.Google Scholar
  37. [37]
    H. D. Choi, C. K. Ahn, M. T. Lim and M. K. Song, “Dynamic output-feedback H control for active half-vehicle suspension systems with time-varying input delay,” International Journal of Control Automation and Systems, vol. 14, no. 1, pp. 59–68, September 2016.CrossRefGoogle Scholar
  38. [38]
    G. Yang and L. Jian, “Reliable guaranteed cost control for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 11, pp. 2188–2192, July 2002.MathSciNetzbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Information EngineeringHenan University of Science and TechnologyHenanChina
  2. 2.School of Electrical and Automation EngineeringNanjing Normal UniversityNanjingChina

Personalised recommendations