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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

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