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

Mark P. Balenzuela

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.

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

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.
Paper Structure (27 sections, 101 equations, 2 figures, 4 algorithms)

This paper contains 27 sections, 101 equations, 2 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. The Jist
  3. Quadratic Programming
  4. Optimising using Sequential Quadratic Programming
  5. Constraints
  6. A QP Solver, Mehrotra's Predictor–Corrector Algorithm
  7. Merit Functions and Line Search Methods
  8. Problem Setup
  9. Forming the Jacobian
  10. Inequality Matrices
  11. Discretisation Method
  12. Discretisation Approach
  13. Algorithm Overview
  14. Results
  15. Analytical Mechanics
  16. ...and 12 more sections

Figures (2)

  • Figure 1: Running the NMPC controller of a cart-pendulum in simulation.
  • Figure 2: The cart pendulum problem.