{"title":"Data-driven stabilization of switched and constrained linear systems","authors":"Mattia Bianchi , Sergio Grammatico , Jorge Cortés","doi":"10.1016/j.automatica.2024.111974","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-10-11","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/S0005109824004680","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
We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures or performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.
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.