Theory, Methods, and Applications of Nonlinear Control Systems with Time Delays

目的：本项目将为重要的确定性非线性控制问题开发最先进的稳定和跟踪方法，以确保在不确定性或时滞下的良好控制器性能。这项工作将包括工程应用，这将指导研究并确保结果的实际用途。其中一个应用将是延迟神经肌肉电刺激模型，这是一种有可能帮助神经系统疾病患者恢复功能的技术。另一个将是与佐治亚理工学院的张付民合作进行水面或水下自动驾驶车辆的实验实时实现。智力优势：由于建模不确定性、传感器设计、耗时的信息处理和传输现象，延迟和不确定性在化学过程控制、燃烧、网络系统、远程操作和其他领域很常见，但它们经常被忽略，以简化分析或因为延迟很短。实际上，许多控制器通常在小不确定性下表现良好，但需要进行严格的分析，以了解干扰如何影响性能，以及在破坏稳定性之前延迟和干扰的大小。本项目将使用自适应或延迟控制器来解决这些关键问题，这些控制器尊重应用程序中经常出现的边界。更广泛的影响：该项目将PI的数学方法与他的工程合作者的工作结合起来。这将增加控制工程界对更严格方法的理解。虽然应用将集中在神经肌肉电刺激和船舶上，但我们预计这项工作将足够普遍，最终将应用于其他对时间延迟很重要的领域，如航空航天和机械工程。该项目还将促进跨学科学习。这项工作将在一个吸引了许多少数民族的机构进行，并将作出特别努力，从代表性不足的群体中招收学生。

Objective: This project will develop cutting edge stabilization and tracking methods for important classes of deterministic nonlinear control problems that ensure good controller performance under uncertainty or time delays. The work will include engineering applications that will guide the research and ensure the practical usefulness of the results. One application will be to a delayed model of neuromuscular electrical stimulation, which is a technique that has the potential to help restore function to patients with neurological disorders. Another will be to experimental real time implementation of surface or underwater autonomous vehicles in collaboration with Fumin Zhang from Georgia Tech.Intellectual Merit: Delays and uncertainty are common in chemical process control, combustion, networked systems, teleoperation, and other areas because of modeling uncertainty, sensor designs, time consuming information processing, and transport phenomena, but they are often ignored to simplify the analysis or because the delays are short. In practice, many controllers typically perform well under small uncertainty, but rigorous analysis is needed to understand how the disturbances impact performance, and how big the delays and disturbances can be before stability is destroyed. This project will address these crucial issues using adaptive or delayed controllers that respect the bounds that often arise in applications.Broader Impacts: The project will combine the PI's mathematical approaches with the work of his engineering collaborators. This will increase the control engineering community's understanding of more rigorous methods. While the applications will focus on neuromuscular electrical stimulation and marine vehicles, we anticipate that the work will be general enough to eventually apply to other areas where time delays are important, such as aerospace and mechanical engineering. The project will also promote interdisciplinary learning. The work will be carried out at an institution that attracts many minorities, and special efforts will be made to recruit students from under- represented groups.