Certified Neural Approximation of Robust Nonlinear Model Predictive Control

Model predictive control is a high-performance control method, but it incurs comparatively high online computational costs across many control tasks and is challenging to realize in low-level hardware settings. To address this, we present a framework for generating neural network controllers that provably inherit the safety and stability guarantees of a robust model predictive policy. In contrast to approaches based on post-verification or additional online safety filters, our method provides constructive, a priori design conditions that ensure preservation of recursive feasibility and stability before deployment. We treat the approximation error as a bounded input disturbance, which is addressed in the MPC design. This allows the neural network controller to directly inherit robustness from the underlying model predictive controller, which enables the transfer of guarantees to the approximation. The design process is an offline, constructive synthesis pipeline and can be implemented once Lipschitz bounds are specified. We further demonstrate in simulation that the learned controller reproduces the closed-loop behavior of the original controller while reducing online computation.