Study Day Dynamical Systems, Control and Optimization location:Leuven, Belgium date:27 November 2009
We present a one-shot multigrid method for the optimal boundary control of time-periodic,
linear, parabolic partial differential equations. We focus on optimal control problems of
the tracking type, i.e., we try to steer the PDE solution such that it matches a prescribed
periodic trajectory, or segment thereof, as closely as possible. To that end we derive the
optimality conditions of such problems. We develop a multigrid method for solving the
resulting coupled system of forward and backward time-periodic equations.