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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Lan Cheng,
  • Ruiyang Cai,
  • Jianping Huang,
  • Huacheng Zhou

摘要

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.