Optimal control problem for deflection plate with crack
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 . 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  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  we get the final result that characterizes the optimal state and control.
Key words and phrasesOptimal control optimality system penalty problem method of bounded increments
2000 Mathematics Subject Classification53C17 22E30 49J15
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