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稳健识别和模型验证该项目寻求开发一个全面的框架，用于获得在需要从海量数据流中提取信息的广泛应用环境中出现的一类非线性系统的数据驱动模型。获得这些模型是开发一类新系统的第一步，该系统具有显著增强的能力，以提取在多模式、极大的数据集中稀疏编码的信息。特别是，作为概念的证明，该项目将侧重于城市环境中的可持续水质管理，这是一个影响发展中国家超过10亿人的问题，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，这一主题将被用来连接从系统论、环境和水文工程到机器学习的各种不同的本科生和研究生课程，重点是稳健性和计算复杂性。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。尽管切换系统的控制在过去几年中取得了长足的进步，但识别和验证适用于这些方法的混杂模型的问题远未解决。本方案旨在通过开发一种易于计算的框架来消除这一差距，以用于切换Hammerstein/Wiener系统的鲁棒辨识和模型验证。它的概念支柱是系统论、半代数几何和凸优化元素的组合，强调稳健性和计算复杂性问题。该方法的主要思想是将切换系统的辨识和模型验证转化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的、计算上易于处理的方法来解决这些问题。该方法的优点包括：(A)解决由于缺乏全面的理论框架和较差的可伸缩性而超出现有技术能力的问题。(B)直接适应和尊重在相关应用领域取得成功的关键特征，如稀疏互连结构。(C)探索系统识别与从非常庞大的数据集中提取可采取行动的信息问题之间迄今基本上未被探索的联系。

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.