Optimal control problem for deflection plate with crack
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2012-07-01
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Springer/plenum Publishers
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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.
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Journal of Dynamical and Control Systems. New York: Springer/plenum Publishers, v. 18, n. 3, p. 397-417, 2012.
