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Resilient \(H_{\infty }\) Filtering for Stochastic Systems with Randomly Occurring Gain Variations, Nonlinearities and Channel Fadings

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Abstract

In this paper, the resilient \(H_{\infty }\) filtering problem for a class of stochastically uncertain discrete-time systems with randomly occurring gain variations, nonlinearities (RONs) and channel fadings is investigated. Considering the existences of random parameter fluctuations in both actual plant and filter, a sequence of mutually independent random variables with known probabilistic distribution is utilized to better describe the stochastic characteristics. The phenomenon RONs, which is regulated by random variables with Bernoulli distribution, is used to reflect the reality that actual systems are generally nonlinear. The system measurement with channel fadings is described by the stochastic Rice fading model, where the channel coefficients are a set of mutually independent random variables with any probability density function. It is worthwhile to mention that a series of slack matrix variables are exploited to eliminate the coupling between the plant matrices and the designed filter parameters by providing free dimensions in the solution space. The purpose of this paper is to design a resilient \(H_{\infty }\) filter such that the filtering error system is asymptotically stable with a prescribed \(H_{\infty }\) performance level. And sufficient conditions for filter design are eventually converted into solving a convex optimization problem over linear matrix inequalities. A numerical example is presented to illustrate effectiveness of the proposed approach.

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References

  1. F. Boem, Y. Zhou, C. Fischione, T. Parisini, Distributed Pareto-optimal state estimation using sensor networks. Automatica 93, 211–223 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Boyd, L. ElGhaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

    Book  Google Scholar 

  3. X.H. Chang, J. Xiong, J. Park, Resilient \({H}_\infty \) filtering for discrete-time systems. Signal Process. 127(C), 71–79 (2016)

    Article  Google Scholar 

  4. B. Chen, L. Yu, W. Zhang, \({H}_\infty \) filtering for Markovian switching genetic regulatory networks with time-delays and stochastic disturbances. Circuits Syst. Signal Process. 30(6), 1231–1252 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Ding, X. Li, Y. Wang, Z. Shi, Non-fragile fuzzy filtering for discrete-time non-linear systems. IET Control Theory Appl. 7(6), 848–857 (2013)

    Article  MathSciNet  Google Scholar 

  6. H. Dong, Z. Wang, D. Ho, H. Gao, Robust \({H}_\infty \) filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case. IEEE Trans. Signal Process. 59(7), 3048–3057 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Dong, Z. Wang, J. Lam, H. Gao, Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts. Int. J. Robust Nonlinear Control 24(12), 1743–1759 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Duan, J. Zhang, C. Zhang, E. Mosca, Robust \({H}_2\) and \({H}_\infty \) filtering for uncertain linear systems. Automatica 42(11), 1919–1926 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. N. Elia, Remote stabilization over fading channels. Syst. Control Lett. 54(3), 237–249 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Jalili, Effective augmentation of networked systems and enhancing pinning controllability. Phys. A 500(15), 155–161 (2018)

    Article  MathSciNet  Google Scholar 

  12. L. Keel, S. Bhattacharyya, Robust, fragile, or optimal ? IEEE Trans. Autom. Control 42(8), 1098–1105 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. J.H. Kim, S.J. Ahn, S. Ahn, Guaranteed cost and \({H}_\infty \) filtering for discrete-time polytopic uncertain systems with time delay. J. Frankl. Inst. 342(4), 365–378 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. C. Lee, I. Fong, \({H}_\infty \) filter design for uncertain discrete-time singular systems via normal transformation. Circuits Syst. Signal Process. 25(4), 525–538 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Z. Li, Z. Wang, D. Ding, H. Shu, Non-fragile \({H}_\infty \) control with randomly occurring gain variations, distributed delays and channel fadings. IET Control Theory Appl. 9(2), 222–231 (2015)

    Article  MathSciNet  Google Scholar 

  16. J. Liu, C. Wu, Z. Wang, L. Wu, Reliable filter design for sensor networks using type-2 fuzzy framework. IEEE Trans. Ind. Inf. 13(4), 1742–1752 (2017)

    Article  Google Scholar 

  17. J. Liu, L. Wu, C. Wu, W. Luo, L.G. Franquelo, Event-triggering dissipative control of switched stochastic systems via sliding mode. Automatica 103, 261–273 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  18. K. Liu, A. Seuret, Y. Xia, Stability analysis of systems with time-varying delays via the second-order Bessel-Legendre inequality. Automatica 76, 138–142 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Lu, J. Tao, P. Shi, H. Su, Z.G. Wu, Y. Xu, Dissipativity-based resilient filtering of periodic Markovian jump neural networks with quantized measurements. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1888–1899 (2018)

    Article  MathSciNet  Google Scholar 

  20. M. Mahmoud, Resilient \({L}_2\)-\({L}_\infty \) filtering of polytopic systems with state delays. IET Control Theory Appl. 1(1), 141–154 (2007)

    Article  MathSciNet  Google Scholar 

  21. K. Nagpal, P. Khargonekar, Filtering and smoothing in an \({H}_\infty \) setting. IEEE Trans. Autom. Control 36(2), 152–166 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  22. I. Petersen, A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8(4), 351–357 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  23. P. Shi, X. Luan, F. Liu, \({H}_\infty \) filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Trans. Ind. Electron. 59(6), 2732–2739 (2012)

    Article  Google Scholar 

  24. C.D. Souza, K. Barbosa, A. Neto, Robust \({H}_\infty \) filtering for discrete-time linear systems with uncertain time-varying parameters. IEEE Trans. Signal Process. 54(6), 2110–2118 (2006)

    Article  MATH  Google Scholar 

  25. G. Sun, L. Wu, Z. Kuang, Z. Ma, J. Liu, Practical tracking control of linear motor via fractional-order sliding mode. Automatica 94, 221–235 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  26. V. Suplin, E. Fridman, U. Shaked, Sampled-data \({H}_\infty \) control and filtering: Nonuniform uncertain sampling. Automatica 43(6), 1072–1083 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Vazquez, A. Marquez, R. Aguilera, D. Quevedo, J. Leon, L. Franquelo, Predictive optimal switching sequence direct power control for grid-connected power converters. IEEE Trans. Ind. Electron. 62(4), 2010–2020 (2015)

    Article  Google Scholar 

  28. Z. Wang, Y. Wang, Y. Liu, Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans. Neural Netw. 21(1), 11–25 (2010)

    Article  Google Scholar 

  29. L. Wu, Y. Gao, J. Liu, H. Li, Event-triggered sliding mode control of stochastic systems via output feedback. Automatica 82, 79–92 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  30. S. Xu, T. Chen, Robust \({H}_\infty \) filtering for uncertain impulsive stochastic systems under sampled measurements. Automatica 39(3), 509–516 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Xu, J. Lam, Y. Zou, \({H}_\infty \) filtering for singular systems. IEEE Trans. Autom. Control 48(12), 2217–2222 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  32. G. Yang, W. Che, Non-fragile \({H}_\infty \) filter design for linear continuous-time systems. Automatica 44(11), 2849–2856 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. H. Yuan, Y. Xia, Secure filtering for stochastic non-linear systems under multiple missing measurements and deception attacks. IET Control Theory Appl. 12(4), 515–523 (2018)

    Article  MathSciNet  Google Scholar 

  34. D. Zhang, W. Cai, L. Xie, Q. Wang, Nonfragile distributed filtering for T-S fuzzy systems in sensor networks. IEEE Trans. Fuzzy Syst. 23(5), 1883–1890 (2015)

    Article  Google Scholar 

  35. D. Zhang, S. Nguang, D. Srinivasan, L. Yu, Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements. IEEE Trans. Fuzzy Syst. 26(3), 1459–1471 (2018)

    Article  Google Scholar 

  36. J. Zhang, X. He, D. Zhou, Robust optimal filtering for linear time-varying systems with stochastic uncertainties. IET Control Theory Appl. 11(18), 3297–3304 (2018)

    Article  MathSciNet  Google Scholar 

  37. Y. Zhang, Z. Wang, L. Ma, Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures. Int. J. Robust Nonlinear Control 26(12), 3507–3523 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  38. Y. Zhang, Z. Wang, L. Zou, Z. Liu, Fault detection filter design for networked multi-rate systems with fading measurements and randomly occurring faults. IET Control Theory Appl. 10(5), 573–581 (2016)

    Article  MathSciNet  Google Scholar 

  39. Y. Zhao, J. Wang, F. Yan, Y. Shen, Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays. Inf. Sci. 473, 227–238 (2019)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors wish to thank the Associate Editor and the anonymous reviewers for their valuable suggestions and comments. This work was supported in part by the National Natural Science Foundation of China and China Academy of Engineering Physics [Grant Number U1530119], in part by the National Natural Science Foundation of China [Grant Number 61741305], in part by the Fundamental Research Funds for the Central Universities [Grant Number HEUCFJ190401], and in part by the China Postdoctoral Science Foundation [Grant Number 2018M63034, 2018T110275].

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  1. College of Automation, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Xiangli Jiang, Guihua Xia & Zhiguang Feng

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  1. Xiangli Jiang
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  2. Guihua Xia
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Correspondence to Zhiguang Feng.

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Jiang, X., Xia, G. & Feng, Z. Resilient \(H_{\infty }\) Filtering for Stochastic Systems with Randomly Occurring Gain Variations, Nonlinearities and Channel Fadings. Circuits Syst Signal Process 38, 4548–4571 (2019). https://doi.org/10.1007/s00034-019-01087-0

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