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# Mapping back and forth between model predictive control and neural networks

*Proceedings of the 6th Annual Learning for Dynamics & Control Conference*, PMLR 242:1228-1240, 2024.

#### Abstract

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