Generic Properties of Conjugate Points in Optimal Control Problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913295875702784 |
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| author | Bressan, Alberto Mazzola, Marco Nguyen, Khai T. |
| author_facet | Bressan, Alberto Mazzola, Marco Nguyen, Khai T. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic Properties of Conjugate Points in Optimal Control Problems Bressan, Alberto Mazzola, Marco Nguyen, Khai T. Optimization and Control 49K05, 49L12 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. |
| title | Generic Properties of Conjugate Points in Optimal Control Problems |
| topic | Optimization and Control 49K05, 49L12 |
| url | https://arxiv.org/abs/2404.02080 |