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Pontryagin Principle for State-Constrained Control Problems Governed by a First-Order PDE System

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Abstract

This paper considers multidimensional control problems governed by a first-order PDE system and state constraints. After performing the standard Young measure relaxation, we are able to prove the Pontryagin principle by means of an ∈-maximum principle. Generalizing the common setting of one-dimensional control theory, we model piecewise-continuous weak derivatives as functions of the first Baire class and obtain regular measures as corresponding multipliers. In a number of corollaries, we derive necessary optimality conditions for local minimizers of the state-constrained problem as well as for global and local minimizers of the unconstrained problem.

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Authors and Affiliations

  1. Institut für Mathematik, Brandenburgische Technische Universität Cottbus, Cottbus, Germany

    S. Pickenhain (Professor of Mathematics)

  2. Institut für Mathematik, Brandenburgische Technische Universität Cottbus, Cottbus, Germany

    M. Wagner (Assistant)

Authors
  1. S. Pickenhain
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  2. M. Wagner
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Pickenhain, S., Wagner, M. Pontryagin Principle for State-Constrained Control Problems Governed by a First-Order PDE System. Journal of Optimization Theory and Applications 107, 297–330 (2000). https://doi.org/10.1023/A:1026481403476

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