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Journal of Dynamical and Control Systems

, Volume 24, Issue 4, pp 635–655 | Cite as

Hierarchical Control for the One-dimensional Plate Equation with a Moving Boundary

  • I. P. de JesusEmail author
  • J. Limaco
  • M. R. Clark
Article
  • 89 Downloads

Abstract

In this paper, we investigate the controllability for the one-dimensional plate equation in intervals with a moving boundary. This equation models the vertical displacement of a point x at time t in a bar with uniform cross section. We assume the ends of the bar with small and uniform variations. More precisely, we have introduced functions α(t) and β(t) modeling the motion of these ends. We present the following results: the existence and uniqueness of Nash equilibrium, the approximate controllability with respect to the leader control, and the optimality system for the leader control.

Keywords

Hierarchical control Stackelberg strategy Approximate controllability Optimality system 

Mathematics Subject Classification (2010)

93B05 93C20 91A23 

Notes

Acknowledgments

We would like to thank the professor L. A. Medeiros by gentle suggestion of this problem and also to professor Marcos Travaglia for his comments on the manuscript. Moreover, the authors are grateful to the anonymous referees for their constructive comments and suggestions, which helped in improving the original manuscript significantly.

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Copyright information

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Authors and Affiliations

  1. 1.Universidade Federal do Piauí, DMTeresinaBrazil
  2. 2.Universidade Federal Fluminense, IMENiteróiBrazil

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