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Stability Analysis of an Optimal Control Problem for a Hyperbolic Equation

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Łódź, Lodz, Poland

    M. Majewski

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  1. M. Majewski
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Correspondence to M. Majewski.

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Communicated by E. Zuazua.

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Majewski, M. Stability Analysis of an Optimal Control Problem for a Hyperbolic Equation. J Optim Theory Appl 141, 127–146 (2009). https://doi.org/10.1007/s10957-008-9504-1

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  • DOI: https://doi.org/10.1007/s10957-008-9504-1

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