Control/Estimation of Free Boundary PDEs


Stefan problem has been known as a thermodynamic model of liquid-solid phase transition since Josef Stefan's work in 1891. While a numerical analysis of the Stefan problem has been considered intensely, the control and estimation problems have been studied relatively fewer in spite of its importance in practical science and engineering. The central goal of my theoretical work is to develop a boundary control and estimation design for the Stefan problem (more generally "free boundary PDEs") via "backstepping design".

Real-Time Optimization by Extremum Seeking Control


Climate Dynamics and Arctic Sea Ice


Arctic sea ice has been studied intensively in the field of climate science. One of the main reasons is due to ice-albedo feedback which influences climate dynamics due to the high reflectivity of sea ice. The other reason is the rapid decline of the Arctic sea ice extent in the recent decade shown in several satellite observations. To predict the future sea ice extent, the online estimation of the sea ice temperature profile is crucial. My goal is to develop an observer algorithm to estimate temperature profile for the Arctic sea ice in a global climate model via some available measurements of sea ice from satellite data.

Battery Management Systems


Lithium Iron Phosphate (LFP) has several attractive features as an active material in lithium-ion batteries such as thermal safety, cost effectiveness, and long cycle life. LFP and other common active materials (e.g. Lithium Cobalt Oxide) show unique charge-discharge characteristics due to an underlying crystallographic solid-solid phase transition. We explore the electrochemical models of the phase transition materials for the single particle model (SPM) where the underlying dynamic model is a partial differential equation (PDE) with a moving boundary. My research is to develop State-of-Charge (SoC) estimation via an observer for the concentration profile of lithium ions from the SPM.