Insights from the application of nonlinear model predictive control to a cart-pendulum

TL;DR

This paper clarifies the mathematics and implementation details of nonlinear model predictive control applied to a cart-pendulum system, making the complex algorithm more accessible and understandable.

Contribution

It provides detailed explanations and elaborations on the nonlinear model predictive control algorithm, which were previously omitted or dense in prior work.

Findings

Enhanced understanding of the control algorithm

Detailed implementation guidance

Clarification of mathematical foundations

Abstract

Inspired greatly by Mills et al. (2009) and the solution within, this paper aims to more clearly explain the mathematics and implementation details of such a powerful control algorithm. While the aforementioned paper is well written and of sound mathematics, it is extreamly dense and requires some time and patience to decipher, especially as it draws on many other sources to complete the algorithm. This dense property is a clear result of the paper being restricted to the brief form and important details being ommited as a result. We provide the much needed elaboration here for the benifit of the reader.