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Risk-sensitive fixed-point smoothing estimation for linear discrete-time systems with multiple output delays

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Abstract

This paper investigates the risk-sensitive fixed-point smoothing estimation for linear discrete-time systems with multiple time-delay measurements. The problem considered can be converted into an optimization one in indefinite space. Then the risk-sensitive fixed-point smoother is obtained by solving the optimization problem via innovation analysis theory in indefinite space. Necessary and sufficient conditions guaranteeing the existence of the risk-sensitive smoother are also given when the risk-sensitive parameter is negative. Compared with the conventional approach, a significant advantage of presented approach is that it provides less computational cost.

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References

  1. Speyer J L, Fan C, and Banavar R N, Optimal stochastic estimation with exponential cost criteria, Proceedings of the IEEE Conf. on Decision and Control, Tucson, 1992.

    Google Scholar 

  2. Fleming W H and Sheu S J, Risk sensitive control and an optimal investment model, Mathematic Finance, 2000, 10(2): 197–213.

    Article  MathSciNet  MATH  Google Scholar 

  3. Whittle P, Risk Sensitive Optimal Control, John Wiley Sons, New York, 1990.

    MATH  Google Scholar 

  4. Speyer J L and Banavar R N, Risk-sensitive estimation and a differential game, IEEE Trans. Automatic Control, 1994, 39(9): 1914–1918.

    Article  MathSciNet  MATH  Google Scholar 

  5. Orguner U and Demirekler M, Risk-sensitive filtering for jump Markov linear systems, Automatica, 2008, 44(1): 109–118.

    Article  MathSciNet  MATH  Google Scholar 

  6. Dey S and Moore J B, Risk-sensitive filtering and smoothing via reference probability methods, IEEE Trans. Automatic Control, 1997, 42(11): 1587–1591.

    Article  MathSciNet  MATH  Google Scholar 

  7. Dey S and Moore J B, Risk-sensitive filtering and smoothing for hidden Markov models, Syste. Contr. Letter, 1995, 25(5): 361–366.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hassibi B, Sayed H A, and Kailath T, Indefinite Quadratic Estimation and Control: A Unified Approach to H 2 and H ∞ Theories, SIAM, New York, 1998.

    Google Scholar 

  9. Zhang H S, Xie L H, and Soh Y C, Risk-sensitive filtering, prediction and smoothing for discretetime singular systems, Automatica, 2003, 39(1): 57–66.

    Article  MathSciNet  MATH  Google Scholar 

  10. Xiao L, Hassibi A, and How J P, Control with random communication delays via a discrete-time jump systems approach, Proceedings of the American Contr. Conference, Chicago, 2000.

    Google Scholar 

  11. Farooq M and Balasubramanian D R, Fixed-interval smoothing of linear discrete systems with multiple time delays, IEEE Trans. Automatic Control, 1976, 21(2): 273–275.

    Article  Google Scholar 

  12. Zhao H G, Zhang H S, and Cui P, Steady-state optimal filtering for continuous systems with time-delay, IEEE Signal Proc. Letter, 2009, 16(7): 628–631.

    Article  Google Scholar 

  13. Zhao H G, Zhang H S, and Zhang C H, Optimal robust estimation for linear uncertain systems with single delayed measurement, Acta Automatica Sinica, 2008, 34(2): 202–207.

    Article  MathSciNet  Google Scholar 

  14. Zhang H S and Xie L H, Control and Estimation of Systems with Input/Output Delays, Springer-Verlag, Berlin, Heidelberg, 2007.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Postdoctoral Research Station of School of Mathematics, Shandong University, Jinan, 250061, China

    Hongguo Zhao

  2. School of Information Science and Technology, Taishan University, Taian, 271021, China

    Hongguo Zhao

  3. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Peng Cui

Authors
  1. Hongguo Zhao
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  2. Peng Cui
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Correspondence to Hongguo Zhao.

Additional information

This research was supported by the National Natural Science Foundations of China under Grant Nos. 61273124, 61174141, China Postdoctoral Science Foundation under Grant No. 2011M501132, Special Funds for Postdoctoral Innovative Projects of Shandong Province under Grant No. 201103043, Doctoral Foundation of Taishan University under Grant No. Y11-2-02, and A Project of Shandong Province Higher Education Science and Technology Program under Grant No. J12LN90.

This paper was recommended for publication by Editor ZHANG Jifeng.

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Zhao, H., Cui, P. Risk-sensitive fixed-point smoothing estimation for linear discrete-time systems with multiple output delays. J Syst Sci Complex 26, 137–150 (2013). https://doi.org/10.1007/s11424-013-1120-y

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  • DOI: https://doi.org/10.1007/s11424-013-1120-y

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