Mapping back and forth between model predictive control and neural networks
This work builds links between model-based and data-driven control, highlighting the potential of implicit neural networks for representing optimization solutions.
The paper demonstrates that model predictive control (MPC) for linear systems with quadratic costs and linear constraints can be exactly represented as an implicit neural network, and introduces a method to convert this into an explicit neural network.
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.