Global Controllability for General Nonlinear Systems

TL;DR

This paper establishes the equivalence of global controllability between general nonlinear systems and their affine extensions, providing a new geometric approach and practical extensions with examples.

Contribution

It introduces a novel geometric method using foliation to analyze controllability, extending results to systems with bounded inputs.

Findings

Global controllability of nonlinear systems is equivalent to that of their affine extensions.

The approach applies to systems with bounded inputs, enhancing practical relevance.

Several illustrative examples demonstrate the effectiveness of the method.

Abstract

This note studies the global controllability of a general nonlinear system by extending it to affine one. The state space of the obtained affine system admits a nature foliation, each leaf of which is diffeomorphic to the state space of the original system. Through this foliation, the global controllability of these two kinds of systems are closely related and we prove that they are indeed equivalent. The result is then extended to the case with bounded inputs to make it practically more useful. To demonstrate the power of our approach, several examples are presented.