Abstract
We provide an improvement of the maximum principle of Pontryagin of the optimal control problems, for a system governed by an ordinary differential equation, in the presence of final constraints, in the setting of the piecewise continuously differentiable state functions (valued in a Banach space) and of piecewise continuous control functions (valued in a metric space). As Michel, we use the needlelike variations, but we introduce tools of functional analysis and a recent multiplier rule of the static optimization to make our proofs.
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The authors thank very much the anonymous referee who has helped us to improve the presentation of the paper.
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Communicated by Dean A. Carlson.
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Blot, J., Yilmaz, H. A Generalization of Michel’s Result on the Pontryagin Maximum Principle. J Optim Theory Appl 183, 792–812 (2019). https://doi.org/10.1007/s10957-019-01587-8
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DOI: https://doi.org/10.1007/s10957-019-01587-8