Optimal Control of a Rotating Body Beam

Weijiu Liu

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

  • 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 (2010): 157-178. <http://eudml.org/doc/90617>.

@article{Liu2010,
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. ; rotating body beam; numerical approximation scheme},
language = {eng},
month = {3},
pages = {157-178},
publisher = {EDP Sciences},
title = {Optimal Control of a Rotating Body Beam},
url = {http://eudml.org/doc/90617},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Liu, Weijiu
TI - Optimal Control of a Rotating Body Beam
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
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. ; rotating body beam; numerical approximation scheme
UR - http://eudml.org/doc/90617
ER -

References

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  10. J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin (1971).  
  11. J.L. Lions and E. Magenes, Non-homogeneous Boundary value Problems and Applications, Vol. I. Springer-Verlag, Berlin, Heidelberg, New York (1972).  Zbl0223.35039
  12. A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York (1983).  Zbl0516.47023
  13. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura Appl. (4)CXLVI (1987) 65-96.  Zbl0629.46031
  14. R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd Ed. Springer-Verlag, New York (1997).  Zbl0871.35001
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