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In this discussion paper we consider the convectiondiffusion equation with time-varying boundary conditions as a simple model of a room whose temperature shall be controlled in an energy efficient way. This model serves as an example for which we want to investigate whether results from a recent paper (Grüne and Pirkelmann, 2017) also hold for a more involved model. In the first part we introduce the model and formulate a constrained optimization problem. The following section outlines how an approximate solution to the problem can be obtained using Model Predictive Control (MPC). The method is briefly described and we also mention results about the relation between the MPC solution and the solution of the original problem. The final part gives a brief overview of selected aspects of the implementation.

Model Predictive Control of a Time-Varying Convection-Diffusion Equation with State Constraints