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

Lan Cheng (), Ruiyang Cai (), Jianping Huang () and Huacheng Zhou ()
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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

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 4, 15 pages

Abstract: 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.

Keywords: Infinite horizon; Quadratic optimal control; Fractional calculus; 49N10; 26A33; 34A08 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02702-8

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