POD-Based Economic Optimal Control of Heat-Convection Phenomena

Abstract

In the setting of energy efficient building operation, an optimal boundary control problem governed by the heat equation with a convection term is considered together with bilateral control and state constraints. The aim is to keep the tem- perature in a prescribed range with the less possible heating cost. In order to gain regular Lagrange multipliers a Lavrentiev regularization for the state constraints is utilized. The regularized optimal control problem is solved by a primal-dual active set strategy (PDASS) which can be interpreted as a semismooth Newton method and, therefore, has a superlinear rate of convergence. To speed up the PDASS a reduced-order approach based on proper orthogonal decomposition (POD) is ap- plied. An a-posterori error analysis ensures that the computed (suboptimal) POD solutions are sufficiently accurate. Numerical test illustates the efficiency of the pro- posed strategy.