Modeling Model Predictive Control: A Category Theoretic Framework for Multistage Control Problems

Understand

Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon.

• In this paper, we introduce a category theoretic framework for constructing complex MPC problem formulations by composing subproblems.
• Specifically, we construct a monoidal category - called Para(Conv) - whose objects are Euclidean spaces and whose morphisms represent constrained convex optimization problems.
• We then show that the multistage structure of typical MPC problems arises from sequential composition in Para(Conv), while parallel composition can be used to model constraints across multiple stages of the prediction horizon.