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Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems

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  • S. Pickenhain

    (Cottbus University of Technology)

  • M. Wagner

    (Cottbus University of Technology)

Abstract

This paper considers multidimensional control problems governed by a first-order PDE system. It is known that, if the structure of the problem is linear-convex, then the so-called ε-maximum principle, a set of necessary optimality conditions involving a perturbation parameter ε > 0, holds. Assuming that the optimal controls are piecewise continuous, we are able to drop the perturbation parameter within the conditions, proving the Pontryagin maximum principle with piecewise regular multipliers (measures). The Lebesgue and Hahn decompositions of the multipliers lead to refined maximum conditions. Our proof is based on the Baire classification of the admissible controls.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:1:d:10.1007_s10957-005-6397-0
    DOI: 10.1007/s10957-005-6397-0
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. C. Udrişte, 2008. "Multitime Controllability, Observability and Bang-Bang Principle," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 141-157, October.

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    1. 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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