Geometry of Cascade Feedback Linearizable Control Systems

TL;DR

This thesis introduces new geometric insights and explicit classes of cascade feedback linearizable control systems, along with obstructions to their existence, advancing the theoretical understanding of control system linearization.

Contribution

It provides a new explicit class of cascade feedback linearizable systems and identifies obstructions to their linearization, based on novel geometric and variational operator techniques.

Findings

New class of cascade feedback linearizable control systems

Obstructions to cascade feedback linearization identified

Connections between geometry and feedback linearization established

Abstract

In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to the existence of a cascade feedback linearization for a given invariant control system. These theorems are presented in Chapter 4, where truncated versions of operators from the calculus of variations are introduced and explored to prove these new results. This connection reveals new geometry behind cascade feedback linearization and establishes a foundation for future exciting work on the subject with important consequences for dynamic feedback linearization.