Sub-Finsler Geodesics on the Cartan Group

    2019, Volume 24, Number 1, pp.  36-60

    Author(s): Ardentov A. A., Le Donne E., Sachkov Y. L.

    This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ 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.
    Keywords: Sub-Finsler geometry, time-optimal control, geometric control, Cartan group
    Citation: Ardentov A. A., Le Donne E., Sachkov Y. L., Sub-Finsler Geodesics on the Cartan Group, Regular and Chaotic Dynamics, 2019, Volume 24, Number 1, pp. 36-60

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