Optimal control of a rotating body beam

Weijiu Liu

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 7, page 157-178
  • ISSN: 1292-8119

Abstract

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In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical approximation scheme to calculate the optimal control and give numeric examples.

How to cite

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Liu, Weijiu. "Optimal control of a rotating body beam." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 157-178. <http://eudml.org/doc/245254>.

@article{Liu2002,
abstract = {In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical approximation scheme to calculate the optimal control and give numeric examples.},
author = {Liu, Weijiu},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {rotating body beam; optimal control; numerical approximation scheme},
language = {eng},
pages = {157-178},
publisher = {EDP-Sciences},
title = {Optimal control of a rotating body beam},
url = {http://eudml.org/doc/245254},
volume = {7},
year = {2002},
}

TY - JOUR
AU - Liu, Weijiu
TI - Optimal control of a rotating body beam
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
PB - EDP-Sciences
VL - 7
SP - 157
EP - 178
AB - In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical approximation scheme to calculate the optimal control and give numeric examples.
LA - eng
KW - rotating body beam; optimal control; numerical approximation scheme
UR - http://eudml.org/doc/245254
ER -

References

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  10. [10] J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1971). Zbl0203.09001MR271512
  11. [11] J.L. Lions and E. Magenes, Non-homogeneous Boundary value Problems and Applications, Vol. I. Springer-Verlag, Berlin, Heidelberg, New York (1972). Zbl0223.35039MR350177
  12. [12] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983). Zbl0516.47023MR710486
  13. [13] J. Simon, Compact sets in the space L p ( 0 , T ; B ) . Ann. Mat. Pura Appl. (4) CXLVI (1987) 65-96. Zbl0629.46031MR916688
  14. [14] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd Ed. Springer-Verlag, New York (1997). Zbl0871.35001MR1441312
  15. [15] C.Z. Xu and J. Baillieul, Stabilizability and stabilization of a rotating body-beam system with torque control. IEEE Trans. Automat. Control 38 (1993) 1754-1765. Zbl0825.93675MR1254313

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