Optimization-based Reference Tracking for Two-Dimensional Multiple Source Heating

In this contribution, we create a model of two-dimensional linear heat conduction with nonlinear boundary conditions as heat transfer and heat radiation. The temperature is steered via multiple actuators on one boundary side, and measurements are taken with multiple sensors on the opposite boundary side. We design with a parametrized input function an optimization-based control strategy to follow a reference trajectory from low to high temperatures. When reaching the desired temperature value, measurements are stabilized at this operating point with a model predictive control technique. Finally, we demonstrate our proposed procedure with a numerical simulation.