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A Model Predictive Control Approach for a Time-Dependent Free-Boundary Problem in Electro-microfluidics

The control of a time-discrete spatially-continuous model of an electrowetting on dielectric (EWOD) device is considered. In this model, contact-angle hysteresis and contact-line pinning is handled macroscopically via a complementarity condition. Due to the complementarity condition on the boundary of the droplet, the resulting control problem represents a type of infinite-dimensional mathematical program with equilibrium constraints (MPEC) with physical and geometric variables. More specifically, velocity, pressure, and voltage are modelled as physical quantities, and the solid-liquid-air interface, i.e., the contact line, arises as an evolving geometric variable. In order to handle the geometric variable both theoretically and numerically, a model predictive control approach is proposed. We derive optimality conditions for the resulting problems at each time step and develop a numerical method based on a projected BFGS scheme. The performance is then demonstrated by several examples.

Type of Seminar:
IfA Seminar
Prof. Thomas M. Surowiec
Humboldt University of Berlin
Jan 13, 2016   4.15 pm

Contact Person:

Prof. John Lygeros
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Biographical Sketch:
Professor Surowiec is currently an assistant professor for non-smooth optimization and variational analysis in the Department of Mathematics at Humboldt-University of Berlin (HUB). From 2009-2014 he was a research associate in the applied mathematics group at HUB. He received his Ph.D. in mathematics from HUB in 2010 and both his B.S. in mathematical sciences and M.S. in stochastic systems and optimization from Stevens Institute of Technology. His research interests include the development of theory and efficient algorithms for optimal control and optimization of partial differential equations (PDE) and variational inequalities, PDE-constrained equilibrium problems, and PDE-constrained optimization under uncertainty using tools from risk management. He is also interested in the application of these results to problems in optics (optimal design of semiconductor lasers) and microfludic devices (controlling electrowetting on dielectric devices).