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Multifidelity Nonsmooth Optimization and Data-Driven Model Reduction for Robust Stabilization of Large-Scale Linear Dynamical Systems

用于大规模线性动力系统鲁棒稳定的多保真非光滑优化和数据驱动模型简化

基本信息

批准号：
2012250
负责人：
Benjamin Peherstorfer
金额：
$ 40万
依托单位：
New York University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-06-01 至 2024-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012250&HistoricalAwards=false
关键词：
Multifidelity Nonsmooth Optimization Data Driven

项目摘要

Autonomous systems play an increasingly important role in engineering applications and in society as a whole, from cars to airplanes to medical devices. Truly autonomous systems will have to be able to act and make decisions under uncertainty. The key component that decides what action an autonomous system takes is the controller of the system, which guarantees that the system always remains in stable and safe states. Thus, designing controllers to stabilize systems is an important problem in a wide range of applications that include virtual or physical systems acting in an environment. The computational methodologies that will be developed in this project aim towards a reliable stabilization of large-scale systems from data alone, even when only little data and data polluted with noise are available. These algorithms have the potential to have significant impact on critical issues such as efficiency, safety, and reliability of autonomous systems. The project will promote cross-disciplinary collaborations from machine learning to control theory to numerical analysis to scientific computing and will support education and diversity by creating novel courses and outreach activities that integrate underrepresented groups in the above disciplines.Robust stabilization typically requires solving nonsmooth, nonconvex optimization problems that are computationally and mathematically challenging. Furthermore, in many situations, models of the systems of interest are unavailable. Rather, data are sampled from the systems and stabilization has to be achieved via learning from these data. This project develops and integrates new methods for nonsmooth optimization via gradient sampling and data-driven (nonintrusive) model reduction via the Loewner framework. The first contribution will be a multifidelity version of the gradient sampling algorithm for nonsmooth optimization that exploits low-cost, low-fidelity gradient approximations of a computationally expensive objective to accelerate the estimation of gradients. If successful, this multifidelity approximation has the potential to make tractable gradient sampling for large-scale optimization problems and at the same time maintain the rigorous convergence guarantees that gradient sampling is known for. The second contribution is to exploit the stability radius of robust controllers to reduce the number of data points (samples) that are required to learn reduced models for stabilizing systems. To that end, a new approach for learning reduced models from data is proposed that allows the learned models to divert from the real system dynamics by as much as can be compensated for by the robustness (stability radius) in favor of reducing the number of data points. If the project is successful, the developed methodologies will enable efficiently and rigorously stabilizing systems that are large-scale and from which few data points and/or high-noise data are available.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

从汽车到飞机再到医疗设备，自主系统在工程应用和整个社会中发挥着越来越重要的作用。真正的自主系统必须能够在不确定的情况下采取行动并做出决定。决定自治系统采取什么行动的关键组件是系统的控制器，它保证系统始终保持在稳定和安全的状态。因此，在包括虚拟或物理系统在内的广泛应用中，设计控制器来稳定系统是一个重要的问题。本项目将开发的计算方法旨在仅凭数据可靠地稳定大型系统，即使只有少量数据和受噪声污染的数据。这些算法有可能对自动化系统的效率、安全性和可靠性等关键问题产生重大影响。该项目将促进从机器学习到控制理论、数值分析到科学计算的跨学科合作，并将通过创建新颖的课程和外展活动来支持教育和多样性，这些课程和外展活动将整合上述学科中代表性不足的群体。鲁棒稳定通常需要解决计算和数学上具有挑战性的非光滑、非凸优化问题。此外，在许多情况下，感兴趣的系统的模型是不可用的。相反，数据是从系统中采样的，必须通过从这些数据中学习来实现稳定。该项目开发并集成了通过梯度采样和通过Loewner框架的数据驱动（非侵入式）模型简化进行非光滑优化的新方法。第一个贡献将是用于非光滑优化的梯度采样算法的多保真度版本，该算法利用计算成本高的目标的低成本，低保真度梯度近似来加速梯度估计。如果成功，这种多保真度近似有可能使大规模优化问题的梯度采样易于处理，同时保持梯度采样所具有的严格收敛性保证。第二个贡献是利用鲁棒控制器的稳定半径来减少学习用于稳定系统的简化模型所需的数据点（样本）的数量。为此，提出了一种从数据中学习简化模型的新方法，该方法允许学习到的模型尽可能多地偏离真实系统动力学，从而可以通过鲁棒性（稳定半径）来补偿，从而有利于减少数据点的数量。如果项目取得成功，所开发的方法将能够有效和严格地稳定大规模的系统，并且可以从很少的数据点和/或高噪声数据中获得。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。