Periodic controls in step 2 strictly convex sub-Finsler problems

DOI10.1134/S1560354720010050zbMath1473.49026arXiv1910.04740OpenAlexW2980209543WikidataQ109746408 ScholiaQ109746408MaRDI QIDQ2176440

Yuri L. Sachkov

Publication date: 4 May 2020

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.04740

zbMATH Keywords

Pontryagin maximum principlestep-2 Carnot groups, sub-Finsler geometrytime-optimal control on Lie groups

Mathematics Subject Classification ID

Optimality conditions for problems involving ordinary differential equations (49K15) Sub-Riemannian geometry (53C17) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (4)

Coadjoint orbits and time-optimal problems for step-2 free nilpotent Lie groups ⋮ Casimir functions of free nilpotent Lie groups of steps 3 and 4 ⋮ Coadjoint orbits of three-step free nilpotent Lie groups and time-optimal control problem ⋮ The isoperimetric problem for regular and crystalline norms in \({\mathbb{H}}^1\)

Cites Work

• Unnamed Item
• Unnamed Item
• Sub-Finsler geodesics on the Cartan group
• Homogeneous manifolds with intrinsic metric. II
• Nilpotent \((3, 6)\) sub-Riemannian problem
• Control theory from the geometric viewpoint.
• The variational maximum principle and second-order optimality conditions for impulse processes and singular processes
• Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups
• Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
• Local (sub)-Finslerian geometry for the maximum norms in dimension 2
• Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher
• Liouville integrability of sub-Riemannian problems on Carnot groups of step 4 or greater
• On the cut locus of free, step two Carnot groups
• Exponential map in the generalized Dido problem
• Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2
• The Isoperimetric Problem in the Minkowski Plane

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