Robust output regulation of the linearized Boussinesq equations with boundary control and observation

We study a temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models for actuation and sensing dynamics; thus, the complete model dynamics are governed by an ODE–PDE–ODE cascade. As the main contribution, we design a low-dimensional internal model-based controller for robust output tracking of the room model. The controller’s performance is demonstrated through a numerical example.