Dimensionless Policies Based on the Buckingham $\pi$ Theorem

This article explores the usage of the Buckingham π theorem as a tool to encode the control policies of physical systems into a more generic form of knowledge that can be reused in various situations. We show that: $a$

• The global problem of learning a global policy for all possible contexts can be simplified in a dimensionless form that involves a lesser number of variables.
• The feedback law solutions of a subset of contexts share the same solution when restated in a dimensionless form, and this can be leveraged to transfer policies exactly between similar context.

Journal article

Girard, A. Dimensionless Policies Based on the Buckingham $\pi$ Theorem: Is This a Good Way to Generalize Numerical Results? Mathematics 2024, 12, 709. https://doi.org/10.3390/math12050709

Preprint on arxiv at this link

Source code

• Python scripts used to generate the numerical results
• Colab page for the pendulum swing-up example
• Colab page for the car example