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A Two-Dimensional Approach to Iterative Learning Control with Randomly Varying Trial Lengths

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Abstract

In this paper, iterative learning control (ILC) is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths. Using the two-dimensional Kalman filtering technique, the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix. It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges. The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method. Numerical simulations are provided to verify the effectiveness of the proposed framework.

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Author information

Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, 100029, China

    Chen Liu

  2. School of Mathematics, Renmin University of China, Beijing, 100872, China

    Dong Shen

  3. Department of Mathematics, Guizhou University, Guiyang, 550025, China

    Jinrong Wang

  4. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Jinrong Wang

Authors
  1. Chen Liu
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  2. Dong Shen
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  3. Jinrong Wang
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Corresponding author

Correspondence to Dong Shen.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 61673045 and 11661016.

This paper was recommended for publication by Editor JIA Yingmin.

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Liu, C., Shen, D. & Wang, J. A Two-Dimensional Approach to Iterative Learning Control with Randomly Varying Trial Lengths. J Syst Sci Complex 33, 685–705 (2020). https://doi.org/10.1007/s11424-020-8215-z

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  • DOI: https://doi.org/10.1007/s11424-020-8215-z

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