DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Harbir Antil, George Mason University

**Title: ***
Finite Horizon Model Predictive Control of Electrowetting on Dielectric with Pinning
*

**Abstract:**
A time-discrete spatially-continuous electrowetting on dielectric
(EWOD) model with contact line pinning is considered as the state
system in an optimal control framework. The pinning model is based on a complementarity condition.
In addition to the physical variables describing velocity, pressure, and voltage, the solid-liquid-air interface, i.e., the contact line, arises as a geometric variable that evolves in time.
Due to the complementarity condition, the resulting optimal control of a free boundary problem is thus a mathematical program with equilibrium constraints (MPEC) in function space.
In order to cope with the geometric variable, a finite horizon model predictive control approach is proposed.
Dual stationarity conditions are derived by applying a regularization
procedure, exploiting techniques from PDE-constrained optimization,
and then passing to the limit in the regularization parameters. Moreover, a function-space-based numerical procedure is developed by following the theoretical limit argument used in the derivation of the dual stationarity conditions. The performance of the algorithm is demonstrated by several examples; including barycenter matching and trajectory tracking.

**Time:** Friday, September 11, 2015, 1:30-2:30 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491