  A robust control scheme is derived and tested for the Navier-Stokes equations
for two-dimensional multiphase flow of a thin film underneath an inclined solid
surface. Control is exerted via the use of an electrode parallel to the
substrate, which induces an electric field in the gas phase, and a resultant
Maxwell stress at the liquid-gas interface. The imposed potential at the second
electrode is derived using a model predictive control loop, together with
optimal control of a high-fidelity reduced-dimensional model. In this
implementation the interfacial shape of the fluid is successfully controlled;
however, the algorithm is sufficiently general to control any other quantity of
interest.
