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Discrete-time mean-field stochastic H 2/H ∞ control

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Abstract

The finite horizon H 2/H ∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic (LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H 2/H ∞ control of meanfield type via the solvability of coupled matrix-valued equations.

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Author information

Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Weihai Zhang & Limin Ma

  2. Science and Information College, Qingdao Agricultural University, Qingdao, 266109, China

    Limin Ma

  3. College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Tianliang Zhang

Authors
  1. Weihai Zhang
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  2. Limin Ma
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  3. Tianliang Zhang
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Corresponding author

Correspondence to Weihai Zhang.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61573227, 61633014, the Research Fund for the Taishan Scholar Project of Shandong Province of China, the SDUST Research Fund under Grant No. 2015TDJH105, and the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources under Grant No. LAPS16011

This paper was recommended for publication by Editor CHEN Jie

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Zhang, W., Ma, L. & Zhang, T. Discrete-time mean-field stochastic H 2/H ∞ control. J Syst Sci Complex 30, 765–781 (2017). https://doi.org/10.1007/s11424-017-5010-6

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  • DOI: https://doi.org/10.1007/s11424-017-5010-6

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