Flat outputs of two-input driftless control systems

Shun-Jie Li; Witold Respondek

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 3, page 774-798
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Li, Shun-Jie, and Respondek, Witold. "Flat outputs of two-input driftless control systems." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 774-798. <http://eudml.org/doc/277812>.

@article{Li2012,
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. },
author = {Li, Shun-Jie, Respondek, Witold},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Control system; flatness; flat output; feedback equivalence; characteristic distribution; n-trailer system; control system; -trailer system},
language = {eng},
month = {11},
number = {3},
pages = {774-798},
publisher = {EDP Sciences},
title = {Flat outputs of two-input driftless control systems},
url = {http://eudml.org/doc/277812},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Li, Shun-Jie
AU - Respondek, Witold
TI - Flat outputs of two-input driftless control systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
PB - EDP Sciences
VL - 18
IS - 3
SP - 774
EP - 798
AB - 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.
LA - eng
KW - Control system; flatness; flat output; feedback equivalence; characteristic distribution; n-trailer system; control system; -trailer system
UR - http://eudml.org/doc/277812
ER -

References

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