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Stochastic LQ Control with Extra Measurability Restriction

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Abstract

Different from the standard linear quadratic (LQ) problem for stochastic systems, the LQ problem considered in the paper has extra measurability restrictions. The problem also appears in the LQ control problem for stochastic systems with delays, rational expectations problems, asymmetric information control, and so on. The essential difficulty lies in that one has to optimize the input and its conditional expectations simultaneously. The stochastic maximum principle (SMP) and orthogonal decomposition technique are the key tools. Firstly, the authors establish the SMP and convert the original problem into forward and backward stochastic difference equations (FBSDEs) with extra measurability restrictions. Secondly, the authors resolve the FBSDEs by using the orthogonal decomposition technique and obtain the analytical solution to the underlying problem. Thirdly, the authors explore the essential distinction between the problem and the standard stochastic LQ control problem. Finally, numerical examples are given to illustrate the obtained results.

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Authors and Affiliations

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

    Hongxia Wang, Yuxi Hu, Zixing Li & Lianfeng Song

Authors
  1. Hongxia Wang
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  2. Yuxi Hu
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  3. Zixing Li
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  4. Lianfeng Song
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Corresponding author

Correspondence to Hongxia Wang.

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The authors declare no conflict of interest.

Additional information

This work was supported by the Original Exploratory Program Project of National Natural Science Foundation of China under Grant No. 62250056, the Joint Funds of the National Natural Science Foundation of China under Grant No. U23A20325, the Major Basic Research of Natural Science Foundation of Shandong Province under Grant No. ZR2021ZD14, and the High-level Talent Team Project of Qingdao West Coast New Area under Grant No. RCTD-JC-2019-05.

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Wang, H., Hu, Y., Li, Z. et al. Stochastic LQ Control with Extra Measurability Restriction. J Syst Sci Complex 37, 1003–1022 (2024). https://doi.org/10.1007/s11424-024-2501-0

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  • DOI: https://doi.org/10.1007/s11424-024-2501-0

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