Control theory is the branch of classical mechanics that deals with 'open systems': physical systems like machines, where the time evolution depends on parameters that can be changed in a time-dependent way by an external agent. We can take small open systems and glue them together to form larger ones. This means that category theory is relevant: we can treat open systems as 'morphisms', and glue them together by composing or tensoring them. Here we describe some small steps toward a category-theoretic approach to control theory.
You can see the slides here. For related material including a video of a talk I gave on control theory, try: