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LQ optimal control of uncertain fractional differential systems

Author

Listed:
  • Zhiwei Wang

    (Nanjing University of Science and Technology)

  • Yuanguo Zhu

    (Nanjing University of Science and Technology)

Abstract

This paper mainly emphasizes the linear quadratic optimal control problem of fractional differential systems based on uncertainty theory, which is an important tool for modeling belief degrees. First, a class of linear uncertain fractional differential equations is solved analytically by solving auxiliary linear uncertain differential equations. Then an equivalent uncertain optimal control model of the uncertain fractional LQ optimal control model is obtained, and the feedback form of its optimal control is deduced by dynamic programming. Finally, a numerical example is analyzed based on the obtained results.

Suggested Citation

  • Zhiwei Wang & Yuanguo Zhu, 2024. "LQ optimal control of uncertain fractional differential systems," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 577-597, December.
    • Handle: RePEc:spr:fuzodm:v:23:y:2024:i:4:d:10.1007_s10700-024-09434-w
    DOI: 10.1007/s10700-024-09434-w
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    References listed on IDEAS

    as
    1. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    2. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    3. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    4. Xiangfeng Yang & Hua Ke, 2023. "Uncertain interest rate model for Shanghai interbank offered rate and pricing of American swaption," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 447-462, September.
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