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AF: Small: Data-Driven Model Reduction for Optimal Control of Large-Scale Systems

AF：小型：用于大型系统优化控制的数据驱动模型简化

基本信息

批准号：
1816219
负责人：
Athanasios Antoulas
金额：
$ 49.94万
依托单位：
William Marsh Rice University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-10-01 至 2022-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1816219&HistoricalAwards=false
关键词：
AF Small Data Driven Model

项目摘要

Dynamical systems are a principal tool in the modeling, prediction, and control of physical phenomena ranging from heat dissipation in complex microelectronic devices, to vibration suppression in large wind turbines, to flow simulation. Optimal control of dynamical systems plays an important role in the many science and engineering applications where one wants to generate inputs to improve the performance of a system. However, ever-increasing need to include more detail at the modeling stage inevitably leads to larger-scale, more complex dynamical systems. Many of these large-scale systems are obtained from spatial discretizations of time-dependent coupled systems of partial differential equations. The simulation of such complex dynamical systems creates huge demands on computational resources and such high fidelity simulations may become unmanageable when the system needs to be queried at many different inputs. This project develops and applies a new class of model reduction methods for the efficient simulation and optimal control of dynamical systems. The model reduction approaches developed in this project approximate large, complex models of time-dependent processes using smaller, computationally efficient models that are nonetheless capable of representing accurately the outputs of the original process under a variety of operating conditions. Thus the new model reduction methods allow simulation and control of systems that would otherwise not be practical with high fidelity computational models.The new model reduction methods developed in this project are data-driven. Unlike existing methods, in many cases, the new methods allow the generation of efficient reduced order computational models directly from (experimental) data and do not require access to high fidelity computational simulations. Overall, this new approach offers several advancements. First, it generates a reduced order model of the original nonlinear dynamical system that is valid for all inputs. Second, the new approach is data-driven and avoids the use of projections. This means less detailed access to the components of the original system are needed, which makes the new method particularly attractive when details of system simulation is inaccessible. This project will develop mathematical algorithms for the creation of such data-driven reduced order models and provide theoretical analyses of their performance. In addition, this project integrates the new model reduction approach into the solution of optimal control problems. For this integration, crucial additional input-output relations will be identified and the reduced order model generation will be augmented to ensure that these additional input-output relations are well approximated. This new approach will be applied to simulation and control of important biological phenomena and of fluid flows.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.

动力系统是建模、预测和控制物理现象的主要工具，这些物理现象包括复杂微电子设备中的散热、大型风力涡轮机中的振动抑制以及流动模拟。动态系统的最优控制在许多科学和工程应用中起着重要的作用，人们希望产生输入来改善系统的性能。然而，在建模阶段包含更多细节的需求不断增加，不可避免地导致更大规模，更复杂的动力系统。这些大规模系统中的许多是从空间离散的时间相关的耦合系统的偏微分方程。这种复杂的动态系统的仿真对计算资源产生了巨大的需求，并且当系统需要在许多不同的输入处被查询时，这种高保真度仿真可能变得难以管理。本计画发展并应用一类新的模型降阶方法，以有效模拟动态系统并进行最佳控制。在这个项目中开发的模型简化方法近似的大型，复杂的模型的时间依赖性的过程，使用较小的，计算效率高的模型，但能够准确地代表各种操作条件下的原始过程的输出。因此，新的模型简化方法允许模拟和控制系统，否则将不实际的高保真计算模型。与现有方法不同，在许多情况下，新方法允许直接从（实验）数据生成有效的降阶计算模型，并且不需要访问高保真度计算模拟。总的来说，这种新方法提供了一些进步。首先，它生成一个降阶模型的原始非线性动态系统，是有效的所有输入。第二，新方法是数据驱动的，避免使用预测。这意味着需要对原始系统的组件进行更少的详细访问，这使得新方法在无法访问系统仿真细节时特别有吸引力。该项目将开发用于创建此类数据驱动降阶模型的数学算法，并对其性能进行理论分析。此外，本计画将新的模型降阶方法整合到最佳控制问题的求解中。对于这种集成，将确定关键的附加输入-输出关系，并且将增强降阶模型生成，以确保这些附加输入-输出关系得到很好的近似。这一新方法将被应用于重要生物现象和流体流动的模拟和控制。该奖项反映了NSF的法定使命，并被认为值得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来支持。