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An Improved Method for Approximating the Infinite-Horizon Value Function of the Discrete-Time Switched LQR Problem

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Abstract

This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem. In particular, the authors propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function. This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration, and thus, the proposed approach is capable of achieving a better approximation for a given computation time compared with the existing methods. Three numerical examples are presented in this paper to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Tan Hou & Yuanlong Li

  2. Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, 200240, China

    Tan Hou & Yuanlong Li

  3. Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai, 200240, China

    Tan Hou & Yuanlong Li

  4. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904-4743, USA

    Tan Hou & Zongli Lin

Authors
  1. Tan Hou
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  2. Yuanlong Li
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  3. Zongli Lin
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Corresponding author

Correspondence to Zongli Lin.

Ethics declarations

LIN Zongli is a Guest Editor of this special issue for Journal of Systems Science & Complexity and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Additional information

This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 62022055 and 61973215.

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Hou, T., Li, Y. & Lin, Z. An Improved Method for Approximating the Infinite-Horizon Value Function of the Discrete-Time Switched LQR Problem. J Syst Sci Complex 37, 22–39 (2024). https://doi.org/10.1007/s11424-024-3422-7

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  • DOI: https://doi.org/10.1007/s11424-024-3422-7

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