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

S. Pickenhain and M. Wagner
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S. Pickenhain: Brandenburgische Technische Universität Cottbus
M. Wagner: Brandenburgische Technische Universität Cottbus

Journal of Optimization Theory and Applications, 2000, vol. 107, issue 2, No 7, 297-330

Abstract: 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.

Keywords: multidimensional control problems; state constraints; Young measure relaxation; Pontryagin principle; first-order necessary conditions; solutions of first Baire class (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1026481403476

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