Sensitivity analysis of hyperbolic optimal control problems

Authors:
Adam Kowalewski;Irena Lasiecka;Jan Sokołowski
Affiliations:
Institute of Automatics, AGH University of Science and Technology, Cracow, Poland 30-059;Department of Mathematics, University of Virginia, Charlottesville, USA 22904-4137 and Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland 01-447;Institut Élie Cartan, UMR 7502 Nancy-Université-CNRS-INRIA, Laboratoire de Mathématiques, Université Henri Poincaré Nancy 1, Vandoeuvre Lès Nancy Cedex, France 54506 ...
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its approximation defined by a suitable Steklov's type differential operator. For approximate optimal control problems the well-posedness is shown. One term asymptotics of optimal control are derived and justified for the approximate model. The key role in the arguments is played by the so called "hidden regularity" of boundary traces generated by hyperbolic solutions.