Scalable Zonotope-Ellipsoid Conversions using the Euclidean Zonotope Norm

Victor Gaßmann, M. Althoff
{"title":"Scalable Zonotope-Ellipsoid Conversions using the Euclidean Zonotope Norm","authors":"Victor Gaßmann, M. Althoff","doi":"10.23919/ACC45564.2020.9147938","DOIUrl":null,"url":null,"abstract":"Set-based computations become increasingly popular for safety-critical systems to ensure properties of controllers and observers. To efficiently compute various set operations, one often uses different set representations and conversions between them. Two popular set representations, for which scalable conversion algorithms do not yet exist, are zonotopes and ellipsoids. We provide computational approaches for all four conversion cases, i.e., overapproximations and underapproximations from zonotopes to ellipsoids and vice versa. By using upper bounds on the maximum and lower bounds on the minimum Euclidean norm of a given zonotope, our approaches have polynomial complexity and thus can be used for high-dimensional spaces. We show that the tightness of our approaches directly depends on the tightness of the Euclidean norm. Numerical experiments demonstrate the usefulness of our proposed methods.","PeriodicalId":288450,"journal":{"name":"2020 American Control Conference (ACC)","volume":"44 4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 American Control Conference (ACC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23919/ACC45564.2020.9147938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7

Abstract

Set-based computations become increasingly popular for safety-critical systems to ensure properties of controllers and observers. To efficiently compute various set operations, one often uses different set representations and conversions between them. Two popular set representations, for which scalable conversion algorithms do not yet exist, are zonotopes and ellipsoids. We provide computational approaches for all four conversion cases, i.e., overapproximations and underapproximations from zonotopes to ellipsoids and vice versa. By using upper bounds on the maximum and lower bounds on the minimum Euclidean norm of a given zonotope, our approaches have polynomial complexity and thus can be used for high-dimensional spaces. We show that the tightness of our approaches directly depends on the tightness of the Euclidean norm. Numerical experiments demonstrate the usefulness of our proposed methods.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
使用欧几里得分区范数的可伸缩分区-椭球体转换
基于集合的计算在安全关键系统中越来越流行,以确保控制器和观测器的属性。为了有效地计算各种集合运算,人们经常使用不同的集合表示和它们之间的转换。两个流行的交涉,可伸缩的转换算法尚不存在,zonotopes椭圆体。我们提供了所有四种转换情况的计算方法,即从分区到椭球体的过逼近和欠逼近,反之亦然。我们的方法利用给定分区的最大范数上界和最小欧氏范数下界,具有多项式复杂度,可用于高维空间。我们证明了我们的方法的紧密性直接取决于欧几里得范数的紧密性。数值实验证明了所提方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Metric Interval Temporal Logic based Reinforcement Learning with Runtime Monitoring and Self-Correction Boundary Control of Coupled Hyperbolic PDEs for Two-dimensional Vibration Suppression of a Deep-sea Construction Vessel Localizing Data Manipulators in Distributed Mode Shape Identification of Power Systems Boundary prescribed–time stabilization of a pair of coupled reaction–diffusion equations An Optimization-Based Iterative Learning Control Design Method for UAV’s Trajectory Tracking
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1