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arXiv · 2404.02080

Generic Properties of Conjugate Points in Optimal Control Problems

Alberto Bressan·Marco Mazzola·Khai T. Nguyen
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Abstract

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 $\psi\in \C^4(\mathbb{R}^n)$, 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.

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Alberto Bressan, Marco Mazzola, Khai T. Nguyen. 2024-04-02. Generic Properties of Conjugate Points in Optimal Control Problems. https://arxiv.org/abs/2404.02080

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