Generic Properties of Conjugate Points in Optimal Control Problems

2024/04/02 by Bressan, Alberto, Mazzola, Marco, Nguyen, Khai T.
#49K05 #49L12 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2404.02080

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 ψ∈ \C⁴(ℝⁿ), 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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