ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2012 - Volume 18, Issue 03  

Research Article

Flat outputs of two-input driftless control systems

Shun-Jie Lia1 and Witold Respondeka1

a1 INSA-Rouen, Laboratoire de Mathématiques, Avenue de l’Université, 76801 Saint-Etienne-du-Rouvray, France. shunjie.li@insa-rouen.fr; witold.respondek@insa-rouen.fr

Abstract

We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all x-flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all x-flat outputs of two-input driftless systems. We illustrate our results by describing all x-flat outputs of models of a nonholonomic car and the n-trailer system.

(Received November 18 2010)

(Online publication October 14 2011)

Key Words:

  • Control system;
  • flatness;
  • flat output;
  • feedback equivalence;
  • characteristic distribution;
  • n-trailer system

Mathematics Subject Classification:

  • 93B27;
  • 93C10;
  • 93C95