Efficient representation and approximation of model predictive control laws via deep learning

TL;DR

This paper demonstrates that deep neural networks can exactly represent and efficiently approximate model predictive control laws for linear systems, enabling deployment on low-power devices with improved accuracy and reduced memory.

Contribution

It provides theoretical bounds for neural network architecture needed to exactly represent MPC laws and shows how deep networks outperform shallow ones in representing complex control laws.

Findings

Deep neural networks can exactly represent MPC laws for linear systems.

Deep networks require fewer parameters than shallow networks for the same task.

The approach enables deployment of advanced control on low-power embedded devices.

Abstract

We show that artificial neural networks with rectifier units as activation functions can exactly represent the piecewise affine function that results from the formulation of model predictive control of linear time-invariant systems. The choice of deep neural networks is particularly interesting as they can represent exponentially many more affine regions compared to networks with only one hidden layer. We provide theoretical bounds on the minimum number of hidden layers and neurons per layer that a neural network should have to exactly represent a given model predictive control law. The proposed approach has a strong potential as an approximation method of predictive control laws, leading to better approximation quality and significantly smaller memory requirements than previous approaches, as we illustrate via simulation examples. We also suggest different alternatives to correct or quantify the approximation error. Since the online evaluation of neural networks is extremely simple, the approximated controllers can be deployed on low-power embedded devices with small storage capacity, enabling the implementation of advanced decision-making strategies for complex cyber-physical systems with limited computing capabilities.