计算平衡点收缩度量的亚梯度算法

IF 1 Q3 Engineering Journal of Computational Dynamics Pub Date : 2023-01-01 DOI:10.3934/jcd.2022030

P. Giesl, S. Hafstein, Magnea Haraldsdottir, D. Thorsteinsson, C. Kawan

{"title":"计算平衡点收缩度量的亚梯度算法","authors":"P. Giesl, S. Hafstein, Magnea Haraldsdottir, D. Thorsteinsson, C. Kawan","doi":"10.3934/jcd.2022030","DOIUrl":null,"url":null,"abstract":". We propose a subgradient algorithm for the computation of contraction metrics for systems with an exponentially stable equilibrium. We show that for sufficiently smooth systems our method is always able to compute a contraction metric on any forward-invariant compact neighbourhood of the equilibrium, which is a subset its basin of attraction. We demonstrate the applicability of our method by constructing contraction metrics for three planar and one three-dimensional systems","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Subgradient algorithm for computing contraction metrics for equilibria\",\"authors\":\"P. Giesl, S. Hafstein, Magnea Haraldsdottir, D. Thorsteinsson, C. Kawan\",\"doi\":\"10.3934/jcd.2022030\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We propose a subgradient algorithm for the computation of contraction metrics for systems with an exponentially stable equilibrium. We show that for sufficiently smooth systems our method is always able to compute a contraction metric on any forward-invariant compact neighbourhood of the equilibrium, which is a subset its basin of attraction. We demonstrate the applicability of our method by constructing contraction metrics for three planar and one three-dimensional systems\",\"PeriodicalId\":37526,\"journal\":{\"name\":\"Journal of Computational Dynamics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/jcd.2022030\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jcd.2022030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}

引用次数: 4

摘要

．我们提出了一种计算具有指数稳定平衡的系统的收缩度量的次梯度算法。我们证明了对于足够光滑的系统，我们的方法总是能够计算平衡的任何正不变紧邻域上的收缩度量，这是它的吸引盆地的一个子集。我们通过构造三个平面和一个三维系统的收缩度量来证明我们方法的适用性

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Subgradient algorithm for computing contraction metrics for equilibria

. We propose a subgradient algorithm for the computation of contraction metrics for systems with an exponentially stable equilibrium. We show that for sufficiently smooth systems our method is always able to compute a contraction metric on any forward-invariant compact neighbourhood of the equilibrium, which is a subset its basin of attraction. We demonstrate the applicability of our method by constructing contraction metrics for three planar and one three-dimensional systems

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.

期刊最新文献

Approximated exponential integrators for the stochastic Manakov equation Dynamical optimal transport of nonlinear control-affine systems Subgradient algorithm for computing contraction metrics for equilibria Convergence of the vertical gradient flow for the Gaussian Monge problem Friction-adaptive descent: A family of dynamics-based optimization methods