CRS--EHS: Collaborartive Research: An Algebraic Geometric Approach to Hybrid Systems Identification

CRS--EHS：协作研究：混合系统识别的代数几何方法

• 批准号: 0509151
• 负责人: Yi Ma
• 金额: $ 15万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2009-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0509151&HistoricalAwards=false
• 关键词: CRS; EHS; Collaborartive; Research; Algebraic

Title: An Algebraic Geometric Approach to Hybrid System IdentificationThe past few years have seen tremendous advances on the analysis, verification, stability, and controllability of systems exhibiting interacting continuous and discrete behavior. However, these advances are strongly based on the assumption that accurate quantitative models are readily available. Relatively less attention has been paid to identification of the model parameters and estimation of the continuous and discrete states of such hybrid systems from input-output data. The intellectual merit of this project is to study fundamental theoretical and computational issues in hybrid system identification from a novel algebraic geometric perspective. The configuration space of a hybrid system is represented as an algebraic variety and its constituent systems as the irreducible components of this variety. Hence, hybrid system identification becomes equivalent to the estimation and decomposition of this variety. This formulation leads to novel batch algorithms for the identification of switched ARX models, jump linear systems, piecewise affine hybrid systems, and classes of nonlinear hybrid systems, together with algebraic conditions under which the provided solutions are unique. The broader impact of the proposed research includes various inference problems across many scientific and engineering fields, such as recognition of human gaits, segmentation of dynamic textures, image/video segmentation, compression, and classification, simultaneous mapping and localization for multiple robots, and modeling of biological networks. Therefore, it is expected that this project will have a broad impact not only in control and systems identification theory, but also in various other disciplines such as algebraic geometry, machine learning, computer vision, and biomedical engineering.

标题：用于混合系统识别的代数几何方法过去几年在分析，验证，稳定性和可控性方面取得了巨大进步，这些系统表现出相互作用的连续和离散行为。但是，这些进步强烈基于以下假设：准确的定量模型很容易获得。从输入输出数据中，对模型参数的识别以及此类混合系统的连续和离散状态的估计的关注相对较少。该项目的智力优点是从新的代数几何学角度研究混合系统识别中的基本理论和计算问题。混合系统的配置空间表示为代数品种，其组成系统是该品种的不可约组件。因此，混合系统识别等于该品种的估计和分解。该公式导致新的批处理算法，用于识别开关ARX模型，跳线线性系统，分段仿射混合系统以及非线性混合系统类别，以及所提供的解决方案独特的代数条件。拟议研究的更广泛的影响包括许多科学和工程领域的各种推理问题，例如识别人类步态，动态纹理的分割，图像/视频细分，压缩和分类，多个机器人的同时映射和本地化以及生物网络的建模。因此，预计该项目不仅在控制和系统识别理论中会产生广泛的影响，而且还将在其他各种学科中（例如代数几何，机器学习，计算机视觉和生物医学工程）产生广泛的影响。