Journal of Dynamical and Control Systems

, Volume 18, Issue 3, pp 397–417 | Cite as

Optimal control problem for deflection plate with crack

  • J. A. D. Chuquipoma
  • C. A. Raposo
  • W. D. Bastos


We consider a control problem where the state variable is defined as the solution of a variational inequality. This system describes the vertical displacement of points of a thin plate with the presence of crack inside [7]. As the control we define the force that originates the deection of the plate. In order to get the system of optimality for the control problem we use a penalized problem [1] and its reformation as a Lagrangian problem. We prove the existence of a Lagrange multiplier to obtain a system of optimality to the exact problem via Lagrangian. Applying the method of bounded increments [19] we get the final result that characterizes the optimal state and control.

Key words and phrases

Optimal control optimality system penalty problem method of bounded increments 

2000 Mathematics Subject Classification

53C17 22E30 49J15 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • J. A. D. Chuquipoma
    • 1
  • C. A. Raposo
    • 1
  • W. D. Bastos
    • 2
  1. 1.Federal University of São João del-ReiDepartament of Mathematics UFSJ - BrazilSão João del-ReiBrazil
  2. 2.São Paulo State UniversityDepartament of Mathematics UNESP - BrazilSão PauloBrazil

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