This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler ℓ∞ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.
Sub-Finsler Geodesics on the Cartan Group
Le Donne, Enrico;
2019-01-01
Abstract
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler ℓ∞ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.File in questo prodotto:
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