On the computation of $\pi$-flat outputs for differential-delay systems

TL;DR

This paper introduces a new concept of π-flatness for linear differential delay systems with time-varying coefficients, providing a characterization and an algorithm for computing flat outputs, demonstrated through an academic motion planning example.

Contribution

It defines π-flatness for differential delay systems, characterizes π-flat outputs, and offers an efficient algorithm for their computation.

Findings

Characterization of π- and π-0-flat outputs

Development of an efficient computation algorithm

Application to an academic motion planning example

Abstract

We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present an academic example of motion planning to discuss the pertinence of the approach.