{"title":"Schatten-p 半径基本椭球的最优性标准和优化,以及对带状椭球和椭球的应用","authors":"Chengrui Wang, Houde Liu, Sanchuan Chen, Feng Xu","doi":"10.1016/j.automatica.2024.111926","DOIUrl":null,"url":null,"abstract":"<div><div>Optimizing a parameterized zonotope or ellipsoid is a common task in robust state estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids and zonotopes into <em>basic ellipsotopes</em>, which support precise representation for more nonlinear boundaries and constraints in practical applications. However, there are currently no available optimality criteria and optimization techniques for general basic ellipsotopes. In this paper, we introduce a novel optimality criterion called <em>Schatten-p radius</em> for basic ellipsotopes. Based on this criterion, we develop a set of methods to minimize the Schatten-<em>p</em> radius under convex constraints for arbitrary <span><math><mrow><mn>0</mn><mo><</mo></mrow></math></span> <em>p</em> <span><math><mrow><mo><</mo><mi>∞</mi></mrow></math></span>, which also implies new available tools for minimizing zonotopes and ellipsoids. The effectiveness of the Schatten-<em>p</em> radius optimization is demonstrated on several numerical examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"171 ","pages":"Article 111926"},"PeriodicalIF":4.8000,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Schatten-p radius: Optimality criterion and optimization for basic ellipsotopes with application to zonotopes and ellipsoids\",\"authors\":\"Chengrui Wang, Houde Liu, Sanchuan Chen, Feng Xu\",\"doi\":\"10.1016/j.automatica.2024.111926\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Optimizing a parameterized zonotope or ellipsoid is a common task in robust state estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids and zonotopes into <em>basic ellipsotopes</em>, which support precise representation for more nonlinear boundaries and constraints in practical applications. However, there are currently no available optimality criteria and optimization techniques for general basic ellipsotopes. In this paper, we introduce a novel optimality criterion called <em>Schatten-p radius</em> for basic ellipsotopes. Based on this criterion, we develop a set of methods to minimize the Schatten-<em>p</em> radius under convex constraints for arbitrary <span><math><mrow><mn>0</mn><mo><</mo></mrow></math></span> <em>p</em> <span><math><mrow><mo><</mo><mi>∞</mi></mrow></math></span>, which also implies new available tools for minimizing zonotopes and ellipsoids. The effectiveness of the Schatten-<em>p</em> radius optimization is demonstrated on several numerical examples.</div></div>\",\"PeriodicalId\":55413,\"journal\":{\"name\":\"Automatica\",\"volume\":\"171 \",\"pages\":\"Article 111926\"},\"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/S0005109824004205\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824004205","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}
Schatten-p radius: Optimality criterion and optimization for basic ellipsotopes with application to zonotopes and ellipsoids
Optimizing a parameterized zonotope or ellipsoid is a common task in robust state estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids and zonotopes into basic ellipsotopes, which support precise representation for more nonlinear boundaries and constraints in practical applications. However, there are currently no available optimality criteria and optimization techniques for general basic ellipsotopes. In this paper, we introduce a novel optimality criterion called Schatten-p radius for basic ellipsotopes. Based on this criterion, we develop a set of methods to minimize the Schatten-p radius under convex constraints for arbitrary p , which also implies new available tools for minimizing zonotopes and ellipsoids. The effectiveness of the Schatten-p radius optimization is demonstrated on several numerical examples.
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.