Reachable sets for contact sub-Lorentzian structures on \(\mathbb R^3\). Application to control affine systems on \(\mathbb R^3\) with a scalar input

DOI10.1007/s10958-011-0464-xzbMath1290.53069OpenAlexW2472099128MaRDI QIDQ2248270

Yanyan Li

Publication date: 25 June 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0464-x

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (16)

Graph surfaces on five-dimensional sub-Lorentzian structures ⋮ 3-dimensional left-invariant sub-Lorentzian contact structures ⋮ The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure ⋮ Remarks on global sub-Lorentzian geometry ⋮ Sub-Lorentzian coarea formula for mappings of Carnot groups ⋮ Sub-Lorentzian distance and spheres on the Heisenberg group ⋮ The area of graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Existence of sub-Lorentzian longest curves ⋮ Classes of maximal surfaces on Carnot groups ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Normal forms for sub-Lorentzian metrics supported on Engel type distributions ⋮ The structure of reachable sets and geometric optimality of singular trajectories for certain affine control systems in \(\mathbb R^{3}\). The sub-Lorentzian approach ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Sub-Lorentzian structures in \(\mathbb {R}^4\): left-invariance and conformal normal forms ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures

Cites Work

• Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
• Properties of reachable sets in the sub-Lorentzian geometry
• Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function
• The Structure of Small-Time Reachable Sets in Low Dimensions
• Contrôlabilité des Systèmes non Linéaires
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