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Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints

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Abstract

A family of parameter dependent optimal control problems is considered. The problems are subject to higher-order inequality type state constraints. It is assumed that, at the reference value of the parameter, the solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some other problems subject to equality type constraints only. The classical implicit function theorem is applied to these new problems to investigate Fréchet dif ferentiability of the stationarity points with respect to the parameter.

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Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul Newelska 6, 01-447, Warszawa, Poland

    Kazimierz Malanowski

  2. Institut für Numerische Mathematik, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149, Münster, Germany

    Helmut Maurer

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  1. Kazimierz Malanowski
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  2. Helmut Maurer
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Malanowski, K., Maurer, H. Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints. Annals of Operations Research 101, 43–73 (2001). https://doi.org/10.1023/A:1010956104457

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