Feedback linearization of nonlinear differential-algebraic control systems

TL;DR

This paper investigates feedback linearization for nonlinear differential-algebraic control systems, providing conditions for linearizability and applying results to examples and mechanical systems.

Contribution

It introduces a new approach using explicitation with driving variables to characterize feedback linearizability of DACSs, linking it to involutivity conditions.

Findings

Necessary and sufficient conditions for feedback linearizability are established.

Feedback linearizability relates to involutivity of linearizability distributions.

Applications include an academic example and a constrained mechanical system.

Abstract

In this paper, we study feedback linearization problems for nonlinear differential-algebraic control systems (DACSs). We consider two kinds of feedback equivalences, namely, the external feedback equivalence, which is defined (locally) on the whole generalized state space, and the internal feedback equivalence, which is defined on the locally maximal controlled invariant submanifold (i.e., on the set where solutions exist). Necessary and sufficient conditions are given for the locally internal and the locally external feedback linearizability of DACSs with the help of a notion called the explicitation with driving variables, which attaches a class of ordinary differential equation control systems (ODECSs) to a given DACS. We show that the feedback linearizability of a DACS is closely related to the involutivity of the linearizability distributions of the explicitation systems. Finally, we apply our results of feedback linearization of DACSs to an academical example and a constrained mechanical system.