Learning an Approximate Model Predictive Controller with Guarantees

TL;DR

This paper introduces a supervised learning framework to approximate model predictive controllers for nonlinear systems, providing stability and constraint guarantees through a combination of robust MPC design and statistical learning bounds.

Contribution

It presents a novel method to train neural network controllers that approximate MPC with formal guarantees on stability and constraints.

Findings

Successfully applied to a nonlinear benchmark problem

Achieved high-confidence guarantees on stability

Reduced computational complexity of MPC

Abstract

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.