Dynamic Equivalence of Control Systems via Infinite Prolongations

TL;DR

This paper explores the dynamic equivalence of control systems using infinite jet bundle pullbacks, extending classification to control affine systems with three states and two controls.

Contribution

It introduces a novel geometric framework for dynamic equivalence and classifies certain control affine systems beyond flat systems.

Findings

Classified all control affine systems with three states and two controls under dynamic equivalence.

Extended the concept of differential flatness to broader control systems.

Provided a geometric approach using infinite jet bundles for control system analysis.

Abstract

In this paper, we put the issue of dynamic equivalence of control systems in the context of pullbacks of coframings on infinite jet bundles over the state manifolds. While much attention has been given to differentially flat systems, i.e. systems dynamically equivalent to linear control systems, the advantage of this approach is that it allowed us to consider control affine systems as well. Through this context we are able to classify all control affine systems of three states and two controls under dynamic equivalence of the type (x,u) |-> y(x,u).