Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays

Frank Woittennek; Joachim Rudolph

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

  • Volume: 9, page 419-435
  • ISSN: 1292-8119

Abstract

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Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński's operational calculus. The method is illustrated through an application to a model of a Timoshenko beam, which is clamped on a rotating disk and carries a load at its free end.

How to cite

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Woittennek, Frank, and Rudolph, Joachim. "Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 419-435. <http://eudml.org/doc/90703>.

@article{Woittennek2010,
abstract = { Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński's operational calculus. The method is illustrated through an application to a model of a Timoshenko beam, which is clamped on a rotating disk and carries a load at its free end. },
author = {Woittennek, Frank, Rudolph, Joachim},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Flatness; motion planning.; linear hyperbolic PDE; finite distributed delays; flatness; motion planning; Timoshenko beam},
language = {eng},
month = {3},
pages = {419-435},
publisher = {EDP Sciences},
title = {Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays},
url = {http://eudml.org/doc/90703},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Woittennek, Frank
AU - Rudolph, Joachim
TI - Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 419
EP - 435
AB - Motion planning and boundary control for a class of linear PDEs with constant coefficients is presented. With the proposed method transitions from rest to rest can be achieved in a prescribed finite time. When parameterizing the system by a flat output, the system trajectories can be calculated from the flat output trajectory by evaluating definite convolution integrals. The compact kernels of the integrals can be calculated using infinite series. Explicit formulae are derived employing Mikusiński's operational calculus. The method is illustrated through an application to a model of a Timoshenko beam, which is clamped on a rotating disk and carries a load at its free end.
LA - eng
KW - Flatness; motion planning.; linear hyperbolic PDE; finite distributed delays; flatness; motion planning; Timoshenko beam
UR - http://eudml.org/doc/90703
ER -

References

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