# Invariant tracking

Philippe Martin; Pierre Rouchon; Joachim Rudolph

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topMartin, Philippe, Rouchon, Pierre, and Rudolph, Joachim. "Invariant tracking." ESAIM: Control, Optimisation and Calculus of Variations 10.1 (2010): 1-13. <http://eudml.org/doc/90719>.

@article{Martin2010,

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.
},

author = {Martin, Philippe, Rouchon, Pierre, Rudolph, Joachim},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Symmetries; invariants; nonlinear control; output
tracking; decoupling.; output tracking; decoupling},

language = {eng},

month = {3},

number = {1},

pages = {1-13},

publisher = {EDP Sciences},

title = {Invariant tracking},

url = {http://eudml.org/doc/90719},

volume = {10},

year = {2010},

}

TY - JOUR

AU - Martin, Philippe

AU - Rouchon, Pierre

AU - Rudolph, Joachim

TI - Invariant tracking

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

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.; output tracking; decoupling

UR - http://eudml.org/doc/90719

ER -

## References

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