Nonlinear Control and Observer Designs for Flow-Transport Systems

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

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, 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.