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.
Mots-clés : flatness, motion planning
@article{COCV_2003__9__419_0,
author = {Woittennek, Frank and Rudolph, Joachim},
title = {Motion planning for a class of boundary controlled linear hyperbolic {PDE's} involving finite distributed delays},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {419--435},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003020},
zbl = {1075.93015},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2003020/}
}
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 PY - 2003 SP - 419 EP - 435 VL - 9 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2003020/ DO - 10.1051/cocv:2003020 LA - en ID - COCV_2003__9__419_0 ER -
%0 Journal Article %A Woittennek, Frank %A Rudolph, Joachim %T Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 419-435 %V 9 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2003020/ %R 10.1051/cocv:2003020 %G en %F COCV_2003__9__419_0
Woittennek, Frank; 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, Tome 9 (2003), pp. 419-435. doi : 10.1051/cocv:2003020. http://archive.numdam.org/articles/10.1051/cocv:2003020/
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