Computational Optimization and Applications

, Volume 52, Issue 1, pp 147–179

Sensitivity analysis of hyperbolic optimal control problems

Open AccessArticle

DOI: 10.1007/s10589-010-9375-x

Cite this article as:
Kowalewski, A., Lasiecka, I. & Sokołowski, J. Comput Optim Appl (2012) 52: 147. doi:10.1007/s10589-010-9375-x


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.


Sensitivity analysisOptimal control problemsHyperbolic boundary value problemsLinear partial differential operatorsSteklov-Poincaré operatorKondratiev weighted spaces
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© 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