Geodesic
Motion planning for a class of boundary controlled linear hyperbolic PDE's involving finite distributed delays
Woittennek, Frank ; Rudolph, Joachim1
1 Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 419-435

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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.

DOI : 10.1051/cocv:2003020
Classification : 35B37, 35L55, 44A40, 93C20
Keywords: flatness, motion planning

Woittennek, Frank  ; Rudolph, Joachim 1

1 Institut fur Regelungs- und Steuerungstheorie, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv:2003020/}
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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

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