Nonlinear Control and Observer Designs for Flow-Transport Systems

了解质量传输，流体混合，以及它们的渐近行为通过反馈控制的流动平流提出了基本的，但极具挑战性的数学问题，在流体动力学，生态学和人口动力学，生物化学工程，工业和系统工程，以及许多其他领域。开发有效的和可操作的协议，最佳的质量传输和混合，传热，并确定属性和长期行为的流动传输相关的动力学模型，特别是在有限的实验数据和/或资源，已引起越来越多的关注，在学术界和工业界。 本研究旨在将这些问题置于一个灵活而严格的数学系统和控制框架内，并基于无限维系统控制和估计工具开发解决策略。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宝贵的跨学科教育，以追求他们未来的研究。该项目将专注于开发非线性反馈定律，该定律利用系统自身状态的信息，控制和稳定的一个广泛的家庭的流动运输问题，新出现在现实世界的应用，包括抑制奇异性的趋化性和淬火的反应扩散。 这样的反馈规律旨在实现实时实现的效率和操纵系统行为的准确性之间的平衡。由于获得完整的状态信息或在时空中的任何地方实现控制通常都是不切实际的，因此本研究将侧重于使用部分系统测量或采样数据，与优化策略一起建立有效的观测器-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。

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.