Article

Computational Optimization and Applications

, Volume 52, Issue 1, pp 147-179

Open Access This content is freely available online to anyone, anywhere at any time.

Sensitivity analysis of hyperbolic optimal control problems

  • Adam KowalewskiAffiliated withInstitute of Automatics, AGH University of Science and Technology
  • , Irena LasieckaAffiliated withDepartment of Mathematics, University of VirginiaSystems Research Institute of the Polish Academy of Sciences
  • , Jan SokołowskiAffiliated withInstitut Élie Cartan, UMR 7502 Nancy-Université-CNRS-INRIA, Laboratoire de Mathématiques, Université Henri Poincaré Nancy 1Systems Research Institute of the Polish Academy of Sciences Email author 

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.

Keywords

Sensitivity analysis Optimal control problems Hyperbolic boundary value problems Linear partial differential operators Steklov-Poincaré operator Kondratiev weighted spaces