Sub-Finsler Geodesics on the Cartan Group
Copyright policy )Sub-Finsler Geodesics on the Cartan Group
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.
26 pages, 47 figures
- University of Pisa Italy
- Program Systems Institute of RAS Russian Federation
- Russian Academy of Sciences Russian Federation
- University of Jyväskylä Finland
Mathematics - Differential Geometry, ta111, matemaattinen optimointi, 49J15; 49K15; Cartan group; geometric control; Sub-Finsler geometry; time-optimal control; Mathematics (miscellaneous), säätöteoria, Differential Geometry (math.DG), geometric control, Optimization and Control (math.OC), FOS: Mathematics, time-optimal control, Matematiikka, differentiaaliyhtälöt, Mathematics - Optimization and Control, Mathematics, Sub-Finsler geometry, Cartan group
Mathematics - Differential Geometry, ta111, matemaattinen optimointi, 49J15; 49K15; Cartan group; geometric control; Sub-Finsler geometry; time-optimal control; Mathematics (miscellaneous), säätöteoria, Differential Geometry (math.DG), geometric control, Optimization and Control (math.OC), FOS: Mathematics, time-optimal control, Matematiikka, differentiaaliyhtälöt, Mathematics - Optimization and Control, Mathematics, Sub-Finsler geometry, Cartan group
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