项目名称: 时滞系统分析与设计:一种解析曲线方法
项目编号: No.61473065
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 自动化技术、计算机技术
项目作者: 李旭光
作者单位: 东北大学
项目金额: 80万元
中文摘要: 本项目提出一种时滞系统分析与设计的新方法:解析曲线方法。该方法基于一系列前期工作,包括若干新数学概念,一致性猜想的证明,和新的频域扫描框架。从解析曲线的新视角,我们将深化时滞系统的研究。 该项目的研究方向包括:(1)首次研究时滞系统解析曲线的代数几何性质。这让我们可以从拓扑角度了解时滞系统,进而对时系统的认知可上升到更高的程度。(2)从宏观的谱特性角度研究时滞系统稳定性和控制器设计问题。我们将获得关于时滞系统的重要新性质。这些新性质将对所研究问题有指导性作用。(3)提出解析曲线方法与计算软件相结合的分析设计思路。该方法可帮助解决过去看来非常棘手的问题同时所得结论不含任何保守性。
中文关键词: 时滞系统;稳定性;解析曲线
英文摘要: We propose a new approach for the analysis and design for time-delay systems: an analytical curve approach. This approach is based on a series of newly-reported results, including new mathematical concepts, the confirmation of the invariance conjecture, and the new frequency-sweeping framework. The objective is to deepen the studies for time-delay systems from the analytical curve perspective. Potential research topics of this project include: (1) We will apply the algebraic geometry to investigate the analytical curves of time-delay systems, for the first time. In this way, we may obtain the topology properties of time-delay systems; (2) We will derive some macro spectral properties related to the analysis and design problems for time-delay systems, which will be instructive for our problems; and (3) We will combine the analytical criterion (based on the analytical curve approach) with algorithms and software. This will make some analysis and design problems, used to be considered intractable, now tractable. Meanwhile, the results involve no conservatism.
英文关键词: time-delay systems;stability;analytical curves