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RESEARCH PRODUCT
Sub-Finsler Geodesics on the Cartan Group
Yuri L. SachkovEnrico Le DonneAndrei Andreevich Ardentovsubject
Mathematics - Differential Geometry0209 industrial biotechnologyPure mathematicsPhysics::General PhysicsGeodesic49K1549J1502 engineering and technology01 natural sciencesContinuationGeneral Relativity and Quantum CosmologyPhysics::Popular Physics020901 industrial engineering & automationMathematics (miscellaneous)Geometric controlFOS: Mathematics0101 mathematicsMathematics - Optimization and ControlMathematics010102 general mathematicsta111matemaattinen optimointiPhysics::History of Physics49J15; 49K15; Cartan group; geometric control; Sub-Finsler geometry; time-optimal control; Mathematics (miscellaneous)säätöteoriaDifferential Geometry (math.DG)Optimization and Control (math.OC)geometric controlNorm (mathematics)Piecewisetime-optimal controldifferentiaaliyhtälötSub-Finsler geometryCartan groupdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-10-12 | Regular and Chaotic Dynamics |