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

Author

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  • S. Pickenhain

    (Brandenburgische Technische Universität Cottbus)

  • M. Wagner

    (Brandenburgische Technische Universität Cottbus)

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.

Suggested Citation

  • S. Pickenhain & M. Wagner, 2000. "Pontryagin Principle for State-Constrained Control Problems Governed by a First-Order PDE System," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 297-330, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026481403476
    DOI: 10.1023/A:1026481403476
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    Cited by:

    1. S. Pickenhain & M. Wagner, 2005. "Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 145-163, October.
    2. M. Wagner, 2009. "Pontryagin’s Maximum Principle for Multidimensional Control Problems in Image Processing," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 543-576, March.

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