Mapping Back and Forth Between Model Predictive Control and Neural Networks

Model predictive control (MPC) for linear systems with quadratic costs andlinear constraints is shown to admit an exact representation as an implicitneural network. A method to "unravel" the implicit neural network of MPC intoan explicit one is also introduced. As well as building links betweenmodel-based and data-driven control, these results emphasize the capability ofimplicit neural networks for representing solutions of optimisation problems,as such problems are themselves implicitly defined functions.