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Bibliographic Details
Main Authors: Bressan, Alberto, Mazzola, Marco, Nguyen, Khai T.
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2404.02080
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Table of Contents:
  • The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, for the optimality of a trajectory which starts at a conjugate point. The second part is concerned with a classical problem in the Calculus of Variations, with free terminal point. For a generic terminal cost $ψ\in \C^4(\mathbb{R}^n)$, applying the previous necessary condition we show that the set of conjugate points is contained in the image of an $(n-2)$-dimensional manifold, and has locally bounded $(n-2)$-dimensional Hausdorff measure.