Linear feedback control and approximation for a system governed by unsteady MHD equations

We are concerned with the feedback control of unsteady flow of an electrically conducting fluid, confined to a bounded region of space and driven by a combination of distributed body force and externally generated currents. The flow is governed by the Navier–Stokes equations and Maxwell’s equations, coupled via Ohm’s law and the Lorentz force. The mathematical formulation and numerical resolution of the linear feedback control problem for tracking velocity and magnetic fields of electrically conducting flows in two dimensional domain are presented. Semi-discrete in time and full space–time discrete approximations are also studied. Computational results showing the efficacy of the feedback control are presented and compared with analogous results using optimal control theory.