33 citations
- University of LiverpoolGB6 papers
- Russian Academy of SciencesRU5 papers
- Eindhoven University of TechnologyNL2 papers
- Institute for Systems AnalysisRU2 papers
- Nanjing University of Science and TechnologyCN2 papers
- Scuola Internazionale Superiore di Studi AvanzatiIT2 papers
- University of JyväskyläFI2 papers
- University of PereslavlRU2 papers
- V. A. Trapeznikov Institute of Control SciencesRU2 papers
- Zhejiang Sci-Tech UniversityCN2 papers
- Centre d'Analyse et de Mathématique SocialesFR1 paper
- Centre National de la Recherche ScientifiqueFR1 paper
42 papers
Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures
A. V. Podobryaev
The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. Th…
One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R)
A. V. Podobryaev
We consider a one-parametric series of left-invariant Lorentzian structures on the universal covering of the Lie group SL(2,R). These structures have SO(1,1)-symmetry and they are…
Sub-Lorentzian extremals defined by an antinorm
A. V. Podobryaev
We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra an…
Existence theorem for sub-Lorentzian problems
L. V. Lokutsievskiy, A. V. Podobryaev
In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We…
Natural differential invariants and equivalence of third order nonlinear differential operators
Valentin Lychagin, Valeriy Yumaguzhin
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and…
Attainable set for rank 3 step 2 free Carnot group with positive controls
A. V. Podobryaev
We find the attainable set for a control system on the free Carnot group of rank and step with positive controls. This kind of control systems is connected with the theory…