{"title":"Adaptive non-cooperative differential games with a regulator","authors":"Nian Liu , Shaolin Tan , Ye Tao , Jinhu Lü","doi":"10.1016/j.automatica.2025.112201","DOIUrl":null,"url":null,"abstract":"<div><div>This paper considers linear–quadratic non-cooperative non-zero-sum stochastic differential games with a regulator and analyzes the adaptive problem when the systems matrices are unknown to both the regulator and the players. It is a typical problem of game-based control systems(GBCS) introduced and studied recently, which have a hierarchical decision-making structure. The main purpose of the paper is to study how the adaptive strategies can be designed to make the GBCS globally stable and at the same time to ensure a Nash equilibrium reached by both the regulator and the players. Under some suitable conditions on the system matrices, it is shown that the closed-loop adaptive GBCS will be globally stable, and at the same time reach a Nash equilibrium by both the regulator and the players, where the adaptive strategies are constructed based on the least squares estimator, the switching method and the diminishing excitation.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"175 ","pages":"Article 112201"},"PeriodicalIF":4.8000,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109825000925","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper considers linear–quadratic non-cooperative non-zero-sum stochastic differential games with a regulator and analyzes the adaptive problem when the systems matrices are unknown to both the regulator and the players. It is a typical problem of game-based control systems(GBCS) introduced and studied recently, which have a hierarchical decision-making structure. The main purpose of the paper is to study how the adaptive strategies can be designed to make the GBCS globally stable and at the same time to ensure a Nash equilibrium reached by both the regulator and the players. Under some suitable conditions on the system matrices, it is shown that the closed-loop adaptive GBCS will be globally stable, and at the same time reach a Nash equilibrium by both the regulator and the players, where the adaptive strategies are constructed based on the least squares estimator, the switching method and the diminishing excitation.
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.
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