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Research Article | Open Access

On the equilibrium strategy of linear-quadratic time-inconsistent control problems

College of Science, Guiyang University, Guiyang 550005, China
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Abstract

The paper investigates the open-loop equilibrium strategy for linear-quadratic time-inconsistent control problems. It derives an equilibrium maximum principle for this strategy and establishes the equivalence among the open-loop equilibrium strategy, two-point boundary value problems, and the equilibrium Riccati equation. Additionally, examples are provided to illustrate the essential differences among the open-loop equilibrium strategy, the closed-loop equilibrium strategy, and the optimal control.

Keywords

equilibrium maximum principleopen-loop equilibrium strategytime-inconsistent cost functionallinear-quadratic control problem
CLC number: 49K15, 49N10, 91B50

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 5480-5494
DOI: 10.3934/math.2025253

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Cite this article:
Ji W. On the equilibrium strategy of linear-quadratic time-inconsistent control problems. AIMS Mathematics, 2025, 10(3): 5480-5494. https://doi.org/10.3934/math.2025253

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Received: 08 October 2024
Revised: 11 February 2025
Accepted: 14 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)