Output-feedback stabilization and control optimization for parabolic equations with Neumann boundary control

Both of feedback stabilization and optimal control problems are analyzed for a parabolic partial differential equation with Neumann boundary control. This PDE serves as a model of heat exchangers in a conducting rod. First, we explicitly construct an output-feedback operator which exponentially stabilizes the abstract control system representing the model. Second, we derive a controller which, simultaneously, stabilizes the associated output an minimizes a suitable cost functional.