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A Note on Infinite Horizon Linear Quadratic Optimal Control Problems for Fractional-order System

Author

Listed:
  • Lan Cheng

    (HNP-LAMA, Central South University)

  • Ruiyang Cai

    (University of Shanghai for Science and Technology)

  • Jianping Huang

    (Hunan University of Science and Technology)

  • Huacheng Zhou

    (HNP-LAMA, Central South University)

Abstract

The practical method for designing a linear quadratic regulator is proposed in [J. Optim. Theory Appl., 174 (2017), 1–17] where the key assumption used is that the optimal control is the linear state feedback control. These results prompt us to ask if this assumption is reasonable. In this note, we show that the optimal control for infinite horizon linear quadratic optimal control of the fractional-order system cannot be produced by linear feedback with a constant gain extracted from the solution of an algebraic Riccatic equation, which is significantly different from the classical result of infinite horizon linear quadratic optimal control for integer order case.

Suggested Citation

  • Lan Cheng & Ruiyang Cai & Jianping Huang & Huacheng Zhou, 2025. "A Note on Infinite Horizon Linear Quadratic Optimal Control Problems for Fractional-order System," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-15, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02702-8
    DOI: 10.1007/s10957-025-02702-8
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    References listed on IDEAS

    as
    1. Chongyang Liu & Zhaohua Gong & Kok Lay Teo & Song Wang, 2022. "Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 856-876, June.
    2. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Gong, Zhaohua & Liu, Chongyang & Teo, Kok Lay & Yi, Xiaopeng, 2022. "Optimal control of nonlinear fractional systems with multiple pantograph‐delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Sara Hatamzadeh Arabi & Farshad Merrikh-Bayat, 2017. "A Practical Method for Designing Linear Quadratic Regulator for Commensurate Fractional-Order Systems," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 550-566, August.
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