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On the H ∞ deconvolution fixed-lag smoothing

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Abstract

The paper deals with the H ∞ deconvolution fixed-lag smoothing problem for a linear timeinvariant discrete-time system with both known and unknown input series. The H ∞ fixed-lag smoother is derived by proposing a new approach termed as re-organized innovation analysis in Krein space. Under the new approach, it is clearly shown that the central deconvolution smoother in an H ∞ setting is the same as the one in an H 2 setting associated with one self-constructed stochastic state-space model. This insight allows us to calculate the complicated H ∞ deconvolution smoother in an intuitive and simple way. The deconvolution smoother is calculated by performing Riccati equation with the same order as the original system.

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Authors and Affiliations

  1. Shandong University, Jinan, 250001, P. R. China

    Xiao Lu & Huanshui Zhang

  2. Shandong University of Science and Technology, Qingdao, 266510, P. R. China

    Xiao Lu

  3. Key Laboratory for Robot & Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao, 266510, P. R. China

    Jie Yan

Authors
  1. Xiao Lu
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  2. Huanshui Zhang
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  3. Jie Yan
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Corresponding author

Correspondence to Xiao Lu.

Additional information

Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il Lee. This work was supported by the National Nature Science Foundation of China (60804034,90920305,60772055), ‘973’ Program (2006CB705506). The work was also supported by the “National Outstanding Youth Foundation” (60825304) and the Nature Science Foundation of Shandong Province (Y2007G34).

Xiao Lu received his B.S. degree from the College of Electron and Information, Dalian Jiaotong University in 1998 and his Ph.D. degree from Dalian University of Technology in 2008. Currently, he is a teacher in Shandong University of Science and Technology. His interests include optimal estimation and control, robust filtering and control, and timedelay systems.

Huanshui Zhang graduated in Mathematics from the Qufu Normal University in 1986 and received his M.Sc. and Ph.D. degrees in Control Theory and Signal Processing from the Heilongjiang University, PR China, and Northeastern University, PR China, in 1991 and 1997, respectively. Currently he is a professor of Shandong University, and is an Associate Editor of IEEE Transactions on Circuits and Systems I.

Jie Yan obtained his Bachelor in Application Physics from Shandong University of Science and Technology, China, in 2007. He is presently toward to a master degree of Shandong University of Science and Technology, China.

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Lu, X., Zhang, H. & Yan, J. On the H ∞ deconvolution fixed-lag smoothing. Int. J. Control Autom. Syst. 8, 896–902 (2010). https://doi.org/10.1007/s12555-010-0424-0

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  • DOI: https://doi.org/10.1007/s12555-010-0424-0

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