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Optimal control for unstructured nonlinear differential-algebraic equations of arbitrary index

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Abstract

We study optimal control problems for general unstructured nonlinear differential-algebraic equations of arbitrary index. In particular, we derive necessary conditions in the case of linear-quadratic control problems and extend them to the general nonlinear case. We also present a Pontryagin maximum principle for general unstructured nonlinear DAEs in the case of restricted controls. Moreover, we discuss the numerical solution of the resulting two-point boundary value problems and present a numerical example.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10–11, 04109, Leipzig, Germany

    Peter Kunkel

  2. Institut für Mathematik, MA 4-5, Technische Universität Berlin, 10623, Berlin, Germany

    Volker Mehrmann

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  1. Peter Kunkel
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  2. Volker Mehrmann
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Correspondence to Volker Mehrmann.

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This research was supported through the Research-in-Pairs Program at Mathematisches Forschungsinstitut Oberwolfach. V. Mehrmann’s research was supported by Deutsche Forschungsgemeinschaft, through Matheon, the DFG Research Center “Mathematics for Key Technologies” in Berlin.

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Kunkel, P., Mehrmann, V. Optimal control for unstructured nonlinear differential-algebraic equations of arbitrary index. Math. Control Signals Syst. 20, 227–269 (2008). https://doi.org/10.1007/s00498-008-0032-1

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