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.
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Pickenhain, S., Wagner, M. Piecewise Continuous Controls in Dieudonné-Rashevsky Type Problems. J Optim Theory Appl 127, 145–163 (2005). https://doi.org/10.1007/s10957-005-6397-0
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DOI: https://doi.org/10.1007/s10957-005-6397-0