Robust Identification and Model Validation for a Class of Nonlinear Dynamic Systems and Applications

一类非线性动态系统和应用的鲁棒识别和模型验证

• 批准号: 1404163
• 负责人: Mario Sznaier
• 金额: $ 38万
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1404163&HistoricalAwards=false
• 关键词: Robust; Identification; Model; Validation; Class

Robust Identification and Model Validation for a Class of Nonlinear Dynamic Systems and ApplicationsThe project seeks to develop a comprehensive framework for obtaining data driven models for a class of nonlinear systems that arise in the context of a broad range of applications that entail extracting information from high volume data streams. Obtaining these models is the first step towards developing a new class of systems with substantially enhanced capabilities to extract information sparsely encoded in multimodal, extremely large data sets. In particular, as a proof of concept, this project will focus on sustainable water quality management in urban environments, a problem that affects over one billion people in the Developing World and leads to losses estimated at over $2 billion/year in the US alone. From an education standpoint, this theme will be used to link a full range of distinct undergraduate and graduate courses, from systems theory, environmental and hydrologic engineering to machine learning, with emphasis on robustness and computational complexity. Undergraduate students will be engaged in research through the OUR Charles (Opportunities for Undergraduate Research on the Charles River) program. While control of switched systems has made considerably progress in the past few years, the problem of identifying and validating hybrid models amenable to be used by these methods is far from solved. The present proposal aims at closing this gap by developing a computationally tractable framework for robust identification and model (in)validation of switched Hammerstein/Wiener systems. Its conceptual backbone is a combination of systems theory, semi-algebraic geometry and convex optimization elements that emphasizes robustness and computational complexity issues. The main idea is to recast the identification and model (in)validation of switched systems into a sparse semi-algebraic optimization form and to exploit recent advances in convex optimization to develop scalable, computationally tractable methods to solve these problems.The advantages of the proposed approach include the ability to: (a) Address problems beyond the capabilities of existing techniques due to a combination of a lack of a comprehensive theoretical framework and poor scaling properties. (b) Directly accommodate and respect features that are key to success in the relevant application domains, such as sparse interconnection structures. (c) Exploit a hitherto largely unexplored connection between systems identification and the problem of extracting actionable information from very large data sets.

一类非线性动态系统和应用的鲁棒辨识和模型验证该项目旨在开发一个全面的框架，用于获得一类非线性系统的数据驱动模型，这些系统在广泛的应用背景下出现，需要从大量数据流中提取信息。 获得这些模型是开发新一类系统的第一步，这些系统具有大幅增强的能力，可以提取在多模态、超大数据集中稀疏编码的信息。特别是，作为概念验证，该项目将侧重于城市环境中的可持续水质管理，这一问题影响到发展中国家的10亿多人，仅在美国每年造成的损失估计就超过20亿美元。 从教育的角度来看，这一主题将用于连接一系列不同的本科和研究生课程，从系统理论，环境和水文工程到机器学习，重点是鲁棒性和计算复杂性。本科生将通过我们的查尔斯（查尔斯河本科生研究机会）计划从事研究。虽然切换系统的控制在过去的几年里取得了相当大的进展，但识别和验证适合这些方法使用的混合模型的问题还远没有解决。本建议旨在通过开发一个计算上易于处理的框架，切换Hammerstein/Wiener系统的鲁棒识别和模型验证，以缩小这一差距。它的概念支柱是系统理论，半代数几何和凸优化元素的组合，强调鲁棒性和计算复杂性问题。 其主要思想是将切换系统的识别和模型验证重新构建为稀疏半代数优化形式，并利用凸优化的最新进展来开发可扩展、计算易处理的方法来解决这些问题。所提出的方法的优点包括能够：（a）解决由于缺乏全面的理论框架和缩放特性差而超出现有技术能力的问题。(b)直接容纳和尊重在相关应用领域中成功的关键功能，例如稀疏互连结构。(c)利用系统识别与从非常大的数据集中提取可操作信息的问题之间迄今为止尚未探索的联系。