Computational Optimization and Applications

, Volume 52, Issue 1, pp 147–179

Sensitivity analysis of hyperbolic optimal control problems

Open Access
Article

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 

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Adam Kowalewski
    • 1
  • Irena Lasiecka
    • 2
    • 4
  • Jan Sokołowski
    • 3
    • 4
  1. 1.Institute of AutomaticsAGH University of Science and TechnologyCracowPoland
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  3. 3.Institut Élie Cartan, UMR 7502 Nancy-Université-CNRS-INRIA, Laboratoire de MathématiquesUniversité Henri Poincaré Nancy 1Vandoeuvre Lès Nancy CedexFrance
  4. 4.Systems Research Institute of the Polish Academy of SciencesWarsawPoland

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