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Causal state feedback representation for infinite horizon LQ problems of fractional systems

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  • Huang, Jianping
  • Zhou, Huacheng

Abstract

In this paper, we consider the feedback representation problem of the optimal control for infinite horizon linear quadratic optimal control problems of fractional systems. By employing the characterization of the optimal control pair and a family of projection operators, we derive the causal state feedback representations which depend only on the history value of the state and does not rely on further state value. Finally, two illustrative examples are included.

Suggested Citation

  • Huang, Jianping & Zhou, Huacheng, 2026. "Causal state feedback representation for infinite horizon LQ problems of fractional systems," Applied Mathematics and Computation, Elsevier, vol. 510(C).
    • Handle: RePEc:eee:apmaco:v:510:y:2026:i:c:s0096300325004187
    DOI: 10.1016/j.amc.2025.129692
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    References listed on IDEAS

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    1. Metzler, Ralf & Glöckle, Walter G. & Nonnenmacher, Theo F., 1994. "Fractional model equation for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(1), pages 13-24.
    2. 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.
    3. 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.
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