Accelerated optimization landscape of linear–quadratic regulator

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-09-28 DOI:10.1016/j.automatica.2024.111927

Lechen Feng, Yuan-Hua Ni

引用次数: 0

Abstract

This paper introduces an accelerated optimization framework of handling the linear–quadratic regulator (LQR) problem. Firstly, a Lipschitz Hessian property of LQR cost is presented, which turns out to be a crucial property for the application of modern optimization techniques. Secondly, a Nesterov-type method with a restarting rule is proposed for state-feedback LQR problem, which can converge exponentially to the optimal feedback gain with Nesterov-optimal order

1 - 1 / \sqrt{κ}

. Thirdly, a Hessian-free two-procedure accelerated framework is proposed for output-feedback LQR problem, which can find an

ϵ

-stationary point with second-order guarantee.

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线性二次调节器的加速优化景观

本文介绍了处理线性二次调节器（LQR）问题的加速优化框架。首先，本文提出了 LQR 成本的 Lipschitz Hessian 特性，该特性对于现代优化技术的应用至关重要。其次，针对状态反馈 LQR 问题提出了一种带有重启规则的内斯特罗夫型方法，该方法可以指数级收敛到最优反馈增益，内斯特罗夫最优阶数为 1-1/κ。第三，针对输出反馈 LQR 问题提出了无黑森二过程加速框架，该框架能在二阶保证下找到ϵ静止点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.