Composing MPC with LQR and Neural Network for Amortized Efficiency and Stable Control

TL;DR

This paper introduces a hybrid control scheme combining MPC, LQR, and neural networks to improve computational efficiency and stability without extensive pre-training, applicable to various dynamical systems.

Contribution

It proposes a novel triple-mode hybrid control scheme that enhances MPC efficiency and stability, avoiding pre-computation and certifying neural network safety.

Findings

Improves amortized running time of MPC with neural networks.

Maintains closed-loop stability with neural networks of proper dimensions.

Applicable to chaotic and slow systems with tailored variants.

Abstract

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we further derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and can improve the amortized running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with any neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications.