Invariant tracking

Philippe Martin; Pierre Rouchon; Joachim Rudolph[1]

  • [1] Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany

ESAIM: Control, Optimisation and Calculus of Variations (2004)

  • Volume: 10, Issue: 1, page 1-13
  • ISSN: 1292-8119

Abstract

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The problem of invariant output tracking is considered: given a control system admitting a symmetry group , design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of . Invariant output errors are defined as a set of scalar invariants of ; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required “symmetry-preserving” feedback.

How to cite

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Martin, Philippe, Rouchon, Pierre, and Rudolph, Joachim. "Invariant tracking." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2004): 1-13. <http://eudml.org/doc/245522>.

@article{Martin2004,
abstract = {The problem of invariant output tracking is considered: given a control system admitting a symmetry group $G$, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of $G$. Invariant output errors are defined as a set of scalar invariants of $G$; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required “symmetry-preserving” feedback.},
affiliation = {Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany},
author = {Martin, Philippe, Rouchon, Pierre, Rudolph, Joachim},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {symmetries; invariants; nonlinear control; output tracking; decoupling; Symmetries},
language = {eng},
number = {1},
pages = {1-13},
publisher = {EDP-Sciences},
title = {Invariant tracking},
url = {http://eudml.org/doc/245522},
volume = {10},
year = {2004},
}

TY - JOUR
AU - Martin, Philippe
AU - Rouchon, Pierre
AU - Rudolph, Joachim
TI - Invariant tracking
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2004
PB - EDP-Sciences
VL - 10
IS - 1
SP - 1
EP - 13
AB - The problem of invariant output tracking is considered: given a control system admitting a symmetry group $G$, design a feedback such that the closed-loop system tracks a desired output reference and is invariant under the action of $G$. Invariant output errors are defined as a set of scalar invariants of $G$; they are calculated with the Cartan moving frame method. It is shown that standard tracking methods based on input-output linearization can be applied to these invariant errors to yield the required “symmetry-preserving” feedback.
LA - eng
KW - symmetries; invariants; nonlinear control; output tracking; decoupling; Symmetries
UR - http://eudml.org/doc/245522
ER -

References

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