Strong well-posedness of the regular linear-quadratic problems: Stabilizable case

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

Automatica Pub Date : 2025-01-30 DOI:10.1016/j.automatica.2025.112145

Renren Zhang

引用次数: 0

Abstract

This paper delves into an open problem within the field of optimal control: the strong well-posedness of the free-endpoint regular indefinite linear quadratic optimal control (LQ). The problem is closely intertwined with the existence of a solution possessing specific properties to an algebraic Riccati equation or inequality. In this paper, some explicit necessary and/or sufficient conditions for the strong well-posedness of the stabilizable case are given, by investigating the existence of a special solution of an algebraic Riccati equation (ARE) corresponding to the LQ and the properties of the minimum solution of an ARE constructed by the controllable part of the system. Additionally, a comparison of the existing sufficient criteria in the literature is provided.

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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.