Black-box modeling and optimal control of a two-phase flow by using navier-stokes equations and level set methods

A modeling and control framework is proposed to describe the behavior of a water-ferrofluid two-phase 2D flow in the presence of a magnetic field and to devise proper optimal control actions. The dynamics of such a system descends from the cascade of magnetic field and Navier-Stokes equations. The former can be dealt with analytically, but this is not possible for the latter, which is usually treated numerically. The description of the motion of the interface between water and ferrofluid is accomplished by using level set methods. To overcome the computational difficulties when controlling such a system, a black-box model based on neural networks is constructed. Different kinds of neural networks are trained to account for the system behavior with an adequate precision in such a way to obtain a model that is well-suited for control. Optimal control is performed by using such black-box models with successful simulation results.