Theory
Control/Estimation of Free Boundary PDEs

Stefan problem has been known as a thermodynamic model of liquidsolid phase transition since Josef Stefan's work in 1891. The Stefan problem is formulated by a diffusion partial differential equation defined on a timevarying spacial domain which obeys an ordinally differential equation driven by Neumann boundary value at the boundary. The statedependency of the boundary makes the implicitly given dynamics of the boundary which is called "free boundary". While a numerical analysis of the Stefan problem has been considered intensely, the control related problems have been studied relatively fewer. The central goal of my theoretical work is to develop a boundary control design for the Stefan problem (more generally "free boundary PDEs") via "backstepping design" which has been intensively advanced in the recent decades.

RealTime Optimization by Extremum Seeking Control
Applications
Additive Manufacturing (3D Printing)
Climate Dynamics and Arctic Sea Ice
Battery Management Systems
