Nonlinear Control and Observer Designs for Flow-Transport Systems

通过平流的反馈控制来理解质量输运、流体混合及其渐近行为，在流体动力学、生态学和种群动力学、生物化学工程、工业和系统工程以及许多其他领域提出了基本但极具挑战性的数学问题。开发有效的、可操作的最佳质量传输和混合、传热协议，以及识别流动传输相关动力学模型的属性和长期行为，特别是在有限的实验数据和/或资源下，已经引起了学术界和工业界越来越多的关注。本研究旨在将这些问题置于一个灵活而严谨的数学系统和控制框架中，并开发基于无限维系统控制和估计工具的解决策略。这项研究将支持研究者的长期职业目标，即通过推进知识和探索现实世界的应用，促进该机构不同研究小组之间的跨学科合作和教育。这项研究也将极大地支持研究者在STEM领域招募和留住学生的努力，特别是那些来自代表性不足的少数民族的学生，并为他们提供坚实的数学训练和有价值的跨学科教育，以追求他们未来的研究。该项目将重点发展非线性反馈定律，利用系统自身状态的信息，控制和稳定在现实世界应用中新出现的一系列流动输运问题，包括抑制趋化性中的奇点和反应扩散的猝灭。这种反馈律的目的是在实时执行的效率和控制系统行为的准确性之间取得平衡。由于获取完整的状态信息和在时空中实现处处控制往往是不现实的，因此本研究将侧重于利用部分系统测量或采样数据，结合优化策略，建立有效的基于观测器的稀疏结构输出反馈控制。该奖项反映了美国国家科学基金会的法定使命，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。

Understanding mass transport, fluid mixing, and their asymptotic behaviors via feedback control of the flow advection poses fundamental yet highly challenging mathematical problems in fluid dynamics, ecology and population dynamics, biochemical engineering, industrial and systems engineering, and many other areas. Developing efficient and operational protocols for optimal mass transport and mixing, heat transfer, and for identifying the attributes and long-time behavior of flow-transport related dynamical models, especially under limited experimental data and/or resources, has attracted increasing attention in both academic and industrial communities. This research aims to place these problems within a flexible and rigorous mathematical system and control framework, and to develop solution strategies based on infinite dimensional system control and estimation tools. This research will support the investigator’s long-term career goals of promoting interdisciplinary collaboration and education among different research groups at the institution by advancing knowledge and exploring real-world applications. This research will also greatly support the investigator's efforts to recruit and retain students in STEM areas, especially those from underrepresented minorities, and to provide them with solid mathematical training and valuable interdisciplinary education to pursue their future studies.The project will focus on the development of nonlinear feedback laws, which utilize information of the system’s own state, for control and stabilization of a broad family of flow-transport problems newly emerged in real-world applications, including suppression of singularity in chemotaxis and quenching of reaction-diffusion. Such feedback laws are aimed at achieving a balance between the efficiency in real-time implementation and the accuracy in steering the system behavior. Since it is often neither practical to obtain the full state information nor to enable control everywhere in space-time, this research will focus on the use of partial system measurement or sampled data, together with optimization strategies to establish the effective observer-based output feedback controls with sparse structure.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.