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Stability Analysis of an Optimal Control Problem for a Hyperbolic Equation

  • M. Majewski
Article

Abstract

In this paper, we derive some results concerning the continuous dependence on parameters of optimal solutions to an optimal control problem that involves a quasilinear hyperbolic differential equation with a boundary condition and a nonlinear integral functional of action; continuous dependence of such kind is sometimes referred to as stability or sensitivity. To present a sufficient condition for the continuous dependence, we use the Kuratowski–Painlevé upper limit of a sequence of sets. Also offered is a technical interpretation of the results.

Keywords

Stability analyses Sensitivity analyses Optimal solutions Optimal control problems Goursat–Darboux problem Kuratowski–Painlevé upper limit 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of ŁódźLodzPoland

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