Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2502.16229

In this paper, the solvability of discrete-time stochastic linear-quadratic (LQ) optimal control problem in finite horizon is considered. Firstly, it shows that the closed-loop solvability for the LQ control problem is optimal if and only if the generalized Riccati equation admits a regular solution by solving the forward and backward difference equations iteratively. To this ends, it finds that the open-loop solvability is strictly weaker than closed-loop solvability, that is, the LQ control problem is always open-loop optimal solvable if it is closed-loop optimal solvable but not vice versa. Secondly, by the perturbation method, it proves that the weak-closed loop strategy which is a feedback form of a state feedback representation is equivalent to the open-loop solvability of the LQ control problem. Finally, an example sheds light on the theoretical results established.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2502.16229
PDF: https://arxiv.org/pdf/2502.16229
OA Status: green
OpenAlex ID: https://openalex.org/W4414838833

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DOI: https://doi.org/10.48550/arxiv.2502.16229

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Title: Weak Closed-loop Solvability for Discrete-time Stochastic Linear-Quadratic Optimal Control

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-02-22

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Authors: Yu-E Sun, Xianping Wu, Xun Li

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Landing page: https://arxiv.org/abs/2502.16229

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PDF URL: https://arxiv.org/pdf/2502.16229

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Cited by: 0

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