CAREER: Constrained Optimal Control of Partial Differential Equations for Improving Energy Utilization in Transportation and in the Built Environment

职业：偏微分方程的约束最优控制，以提高交通和建筑环境中的能源利用率

基本信息

批准号：
2042354
负责人：
Stephanie Stockar
金额：
$ 67.51万
依托单位：
Ohio State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-08-15 至 2026-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2042354&HistoricalAwards=false
关键词：
CAREER Constrained Optimal Control Partial

项目摘要

This Faculty Early Career Development (CAREER) award will lead to the creation of a new mathematical framework for the solution of optimal control problems with input and state constraints in systems described by Partial Differential Equations. Partial Differential Equations are relevant to several engineering fields, such as electrochemical and thermal energy storage, energy distribution and conversion, and are frequently used to predict traffic flows in transportation. Application of optimal control to such Partial Differential Equations systems will lead to a significant reduction in the energy utilization and improve sustainability in the residential and transportation sectors, however such benefits are contingent upon the ability of the control algorithm to satisfy input and state constraints. This work will establish an emerging and interdisciplinary research program that bridges across thermal and fluid sciences, control theory, modeling and simulation. This award will support the educational goal of mentoring and motivating undergraduate students in pursuing a research experience by starting a new program targeting Sophomore and Junior Mechanical Engineering students. This initiative will support the retention of students in their program of choice, particularly from underrepresented groups, and will result in larger number of domestic students pursuing graduate education.This research will lead to the creation of a theory and methods to obtain approximate solutions of constrained optimal control problems for Partial Differential Equations. The established practice relies on a two-steps process, in which the plant is first discretized to a finite dimensional system, then the controller is designed on the reduced order model. This research will overcome the theoretical and practical limitations of conventional methods, leading to (i) controllers that do not require calibration to compensate for model approximations; (ii) guaranteed satisfaction of constraints on the infinite dimensional system; (iii) eliminating the need to develop reduced plant models. The enabling mathematical tool to achieve this goal is the derivation of an approximate solution of the Hamilton-Jacobi-Bellman equation via parametrization of the value function, which is a central contribution of this research. Ultimately, this project will (i) advance the theory of constrained optimal control of Partial Differential Equations, through transformative methods for the parametric solution of the Hamilton-Jacobi-Bellman equation via reduction; (ii) advance the understanding of constrained control of large scale system, by interpreting them as finite-order approximations of infinite dimensional systems; (iii) develop methods for practical, online implementation of state feedback controllers for systems described by Partial Differential Equations.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.

这项教师早期职业发展（职业）奖将导致创建一个新的数学框架，以解决由部分微分方程描述的系统中的最佳控制问题解决最佳控制问题。部分微分方程与几个工程领域有关，例如电化学和热能存储，能量分布和转换，并且经常用于预测运输中的交通流。最佳控制在此类部分微分方程系统上的应用将显着降低能源利用率并改善住宅和运输部门的可持续性，但是这种好处取决于控制算法满足输入和状态约束的能力。这项工作将建立一个新兴和跨学科的研究计划，该计划桥梁跨热科学，控制理论，建模和仿真。该奖项将支持指导和激励本科生通过启动针对大二和初级机械工程专业学生的新计划来追求研究经验的教育目标。该倡议将支持学生在其首选计划中的保留，尤其是来自代表性不足的群体，并将导致更多的家庭学生接受研究生教育。这项研究将导致创建一种理论和方法，以获取针对部分微分方程的约束最佳控制问题的近似解决方案。既定的实践依赖于两个步骤的过程，在该过程中首先将工厂离散为有限的维度系统，然后在还原订单模型上设计控制器。这项研究将克服常规方法的理论和实际局限性，从而导致（i）不需要校准来补偿模型近似值的控制器；（ii）保证对无限尺寸系统的约束满意；（iii）消除了开发减少植物模型的需求。实现这一目标的启用数学工具是通过值函数的参数化来推导汉密尔顿 - 雅各比 - 贝尔曼方程的近似解，这是这项研究的核心贡献。最终，该项目（i）通过减少汉密尔顿 - 雅各比 - 贝尔曼方程的参数解决方案的变换方法（i）将推进对部分微分方程的最佳控制理论。（ii）通过将其解释为无限尺寸系统的有限级近似值来推进对大规模系统的受限控制的理解；（iii）开发了针对部分微分方程所描述的系统的实用，在线实施国家反馈控制器的方法。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。