CAREER: An Efficient Computational Framework for Data Driven Feedback Control

最优控制是一项数学挑战，旨在找到引导受控系统实现最优成本性能的控制动作。大多数现有的最优控制方法假设受控系统的状态是完全可观察的，因此来自受控状态的反馈是明确可用的。然而，在许多实际情况下，被控系统是不可直接观测的。在这个项目中，研究者的目标是开发有效和准确的数据同化方法来分析间接观测数据，并构建一个有效的计算框架，根据观测数据中包含的信息设计最优控制。这种新的框架有可能有利于纳米级的控制和设计材料，以及各种规模的电力系统的控制，以支持可靠和高效的电网。该项目包括培训下一代数据科学家的活动，这些数据科学家具有数学洞察力和技术技能，以应对重要的实际挑战。该项目的目标是开发一个高效的计算框架，使数据能够最佳地驱动控制动作。主要工作将致力于数据驱动的最优控制方法的发展，将最先进的数据同化方法纳入随机最优控制求解器。在这个项目中进行的研究还旨在阐明数据和行动之间的内在联系。这项研究有两个重点。第一个推力将集中在数学和计算方法的发展，以建立一个有效的数据驱动的反馈控制框架。然后，在第一次推进中开发的方法将应用于解决第二次推进中的实际科学和工程反馈控制问题。该奖项反映了NSF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。

Optimal control is a mathematical challenge that aims to find control actions that guide a controlled system to achieve optimal-cost performance. Most existing methods for optimal control assume that the state of the controlled system is fully observed, and therefore that the feedback from the controlled state is explicitly available. In many practical cases, however, the controlled system is not directly observable. In this project, the investigator aims to develop efficient and accurate data assimilation methods to analyze indirect observational data and to construct an efficient computational framework to design optimal control based on the information contained in the observational data. This new framework has the potential to benefit the control and design materials at the nano-scale as well as the controls of power systems at various scales to support reliable and an efficient electric grid. The project incorporates activities to train the next generation of data scientists with both mathematical insight and technical skills to address important practical challenges.The goal of this project is to develop an efficient computational framework that will allow data to optimally drive control actions. The primary efforts will be dedicated to the development of data driven optimal control methods, incorporating state-of-the-art data assimilation methods into stochastic optimal control solvers. The research carried out in this project also aims to elucidate inherent connections between data and actions. The research has two thrusts. The first thrust will focus on the development of mathematical and computational methods to establish an efficient data driven feedback control framework. Then, the methods developed in the first thrust will be applied to solve practical scientific and engineering feedback control problems in the second thrust.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.