Collaborative Research: Sequential Predictors for Partial Differential Equation and Delay Systems: Designs, Theory, and Applications

合作研究：偏微分方程和延迟系统的序贯预测器：设计、理论和应用

• 批准号: 1711373
• 负责人: Miroslav Krstic
• 金额: $ 22万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1711373&HistoricalAwards=false
• 关键词: Collaborative; Research; Sequential; Predictors; Partial

This project solves the problem of implementability of feedback controls for a variety of dynamical systems that arise in additive manufacturing, battery modeling, deep mine elevators, oil drilling, traffic congestion, water desalination, and other engineering domains. Feedback control involves the use of information about the states of dynamical systems and about their surroundings, to decide how to adjust the behavior of the systems to realize important objectives such as ensuring that the systems safely converge to a desirable operating mode with minimal human intervention. The project combines the PIs' complementary expertise in engineering and mathematics, by tackling important interdisciplinary problems that could not be solved outside of this new collaborative framework. The project studies interconnected systems with delays, in which the current states of the systems or of their surroundings may not be available for use in the feedback control design, and related problems in extremum seeking under delays, in which one wishes to minimize important types of cost criteria. Through the PIs' contacts with engineers from industry, the project will increase the engineering community's use of more rigorous methods to obtain better performing controls and will also provide interdisciplinary training to graduate students that is guided by compelling engineering applications.The project provides transformative control and extremum seeking algorithms for key classes of ODE and ODE-PDE cascades that involve delays, prescribed regulation times, and uncertainties. Input delays arise from sensor or transport phenomena, and finite time constraints occur when there are hard deadlines for achieving control objectives. While prediction has been used extensively, there are currently no analogs of prediction for stabilization problems with prescribed regulation times where there are delays and uncertain model parameters. This project overcomes these challenges for general classes of nonlinear systems, using new sequential predictors, sequential anti-diffusors, chain observers, adaptive control with parameter identification, and extremum seeking under delays or time constraints, including cases where only sampled output measurements are available. The controls developed ensure better disturbance rejection and robustness against uncertainties. The project is guided by cutting edge engineering applications, to ensure the usefulness of the theory. They involve models for underwater marine robots where slow acoustic communication is modeled through long delays, the reduction of severe slugging in oil production, and online social networks where opinion spreading is modeled by PDE-ODE cascades with diffusion. The project will include experimental real time implementation of some of the controls and train PhD students.

该项目解决了增材制造、电池建模、深井电梯、石油钻井、交通拥堵、海水淡化和其他工程领域中出现的各种动力系统的反馈控制的可实施性问题。反馈控制涉及使用有关动态系统状态及其周围环境的信息，来决定如何调整系统的行为以实现重要目标，例如确保系统以最少的人为干预安全地收敛到所需的操作模式。该项目结合了 PI 在工程和数学方面的互补专业知识，解决了在这个新的协作框架之外无法解决的重要跨学科问题。该项目研究具有延迟的互连系统，其中系统或其周围环境的当前状态可能无法用于反馈控制设计，以及延迟下极值搜索的相关问题，其中人们希望最小化重要类型的成本标准。通过 PI 与业界工程师的接触，该项目将增加工程界使用更严格的方法来获得性能更好的控制，并将为研究生提供以引人注目的工程应用为指导的跨学科培训。该项目为 ODE 和 ODE-PDE 级联的关键类别提供变换控制和极值搜索算法，这些级联涉及延迟、规定的调节时间和不确定性。输入延迟是由传感器或传输现象引起的，当实现控制目标存在严格的最后期限时，就会出现有限的时间限制。虽然预测已被广泛使用，但目前还没有类似的预测来预测具有规定调节时间的稳定问题，其中存在延迟和不确定的模型参数。该项目克服了一般类别非线性系统的这些挑战，使用新的顺序预测器、顺序反扩散器、链观察器、具有参数识别的自适应控制以及延迟或时间限制下的极值搜索，包括仅提供采样输出测量的情况。开发的控制确保更好的干扰抑制和针对不确定性的鲁棒性。该项目以前沿工程应用为指导，以确保理论的实用性。它们涉及水下海洋机器人模型，其中通过长延迟、减少石油生产中的严重塞击来模拟缓慢的声学通信，以及通过带有扩散的 PDE-ODE 级联来模拟意见传播的在线社交网络。该项目将包括一些控制的实验性实时实施并培训博士生。