Collaborative Research: Piecewise Linear Hybrid Systems

合作研究：分段线性混合系统

• 批准号: 0206795
• 负责人: Bhaskar DasGupta
• 金额: $ 10万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0206795&HistoricalAwards=false
• 关键词: Collaborative; Research; Piecewise; Linear; Hybrid

This proposal deals with the design and analysis of efficient algorithms forthe class of hybrid systems called (discrete-time) piecewise linear (PL)systems. The area of hybrid systems concerns issues of modeling, computation andcontrol for systems which combine discrete and continuous components.The subclass of PL systems, which we investigate in this project,provides one systematic approachto discrete-time hybrid systems, naturally blending switching mechanisms withclassical linear components.PL systems are of interest as controllers as well as identification models,and they can be thought of as arbitrary interconnections of finite automataand linear systems. Tools from automata theory, logic and related areas of computerscience and finite mathematics are used in the study of PL systems, inconjunction with linear algebra techniques, all in the context of a ``PLalgebra'' formalism. In this project, we will study basic algorithmicand computational problems for these problems with applications tomodelling of biological systems.More concretely, basic questions for any class of systems are those of equivalence, and, inparticular, whether state spaces are equivalent under a change of variables.This project will address various algorithmic and computational challengesrelated to this state-space equivalence and isomorphism problem for PLsystems, as well as questions of learnability and representability for suchsystems. The project also suggests the use of PL models for differential geneexpression testing.

该提案涉及称为（离散时间）分段线性（PL）系统的混合系统类的有效算法的设计和分析。混合系统领域涉及结合离散和连续组件的系统的建模、计算和控制问题。我们在本项目中研究的 PL 系统的子类为离散时间混合系统提供了一种系统方法，自然地将开关机制与经典线性混合在一起PL 系统作为控制器和识别模型很受关注，它们可以被认为是有限自动机和线性系统的任意互连。自动机理论、逻辑以及计算机科学和有限数学相关领域的工具与线性代数技术结合用于 PL 系统的研究，所有这些都在“PLalg​​ebra”形式主义的背景下进行。在这个项目中，我们将研究这些问题的基本算法和计算问题，并将其应用于生物系统建模。更具体地说，任何一类系统的基本问题都是等价问题，特别是状态空间在变量变化下是否等价该项目将解决与 PL 系统的状态空间等价和同构问题相关的各种算法和计算挑战，以及此类系统的可学习性和可表示性问题。该项目还建议使用 PL 模型进行差异基因表达测试。