Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification

TL;DR

This paper develops a method to bound approximation errors in neural network-based imitation MPC controllers using Lipschitz properties, enhancing stability and performance guarantees through dataset design and training adjustments.

Contribution

It introduces a novel error bounding framework for neural network imitation MPC, guiding dataset creation and training to improve stability and accuracy.

Findings

Error bounds effectively guide dataset design.

Training adjustments reduce dataset density needs.

Improved closed-loop behavior in simulations.

Abstract

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.