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- Title
Generic properties of conjugate points in optimal control problems.
- Authors
Bressan, Alberto; Mazzola, Marco; Nguyen, Khai T.
- 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 {{\mathcal 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.
- Subjects
HAUSDORFF measures; POINT set theory; COST
- Publication
Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1
- ISSN
2156-8472
- Publication type
Academic Journal
- DOI
10.3934/mcrf.2024042