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.

翻译：线性系统下具有二次成本和线性约束的模型预测控制（MPC）被证明可以精确表示为隐式神经网络。本文还提出了一种将MPC的隐式神经网络"解耦"为显式神经网络的方法。这些结果不仅建立了基于模型控制与数据驱动控制之间的联系，还突显了隐式神经网络在表示优化问题解方面的能力——因为此类问题本身即为隐式定义的函数。