We study the optimal control problem of a second order linear evolution equation defined in two-component composites with epsilon-periodic disconnected inclusions of size epsilon in presence of a jump of the solution on the interface that varies according to a parameter gamma. In particular here the case gamma<1 is analyzed. The optimal control theory, introduced by Lions, leads us to characterize the control as the solution of a set of equations, called optimality conditions. The main result of this paper proves that the optimal control of the epsilon-problem, which is the unique minimum point of a quadratic cost functional at epsilon level, converges to the optimal control of the homogenized problem with respect to a suitable limit cost functional. The main difficulties are to find the appropriate limit functional for the control of the homogenized system and to identify the limit of the controls.

Optimal control for evolutionary imperfect transmission problems

Perugia C.
2015

Abstract

We study the optimal control problem of a second order linear evolution equation defined in two-component composites with epsilon-periodic disconnected inclusions of size epsilon in presence of a jump of the solution on the interface that varies according to a parameter gamma. In particular here the case gamma<1 is analyzed. The optimal control theory, introduced by Lions, leads us to characterize the control as the solution of a set of equations, called optimality conditions. The main result of this paper proves that the optimal control of the epsilon-problem, which is the unique minimum point of a quadratic cost functional at epsilon level, converges to the optimal control of the homogenized problem with respect to a suitable limit cost functional. The main difficulties are to find the appropriate limit functional for the control of the homogenized system and to identify the limit of the controls.
optimal control; homogenization; evolution equations
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/6021
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