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Stability Analysis of an Optimal Control Problem for a Hyperbolic Equation

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  • M. Majewski

    (University of Łódź)

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.

Suggested Citation

  • M. Majewski, 2009. "Stability Analysis of an Optimal Control Problem for a Hyperbolic Equation," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 127-146, April.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9504-1
    DOI: 10.1007/s10957-008-9504-1
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    References listed on IDEAS

    as
    1. M. Majewski, 2006. "On the Existence of Optimal Solutions to an Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 635-651, March.
    2. S. Walczak, 2001. "Well-Posed and Ill-Posed Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 169-185, April.
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