Journal of Mathematical Sciences

, 177:383 | Cite as

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



In this paper, we investigate the structure of reachable sets for general contact sub-Lorentzian metrics on \( {\mathbb{R}^3} \). In some particular cases, the presented method leads to explicit formulas for functions describing reachable sets. We also compute the image under exponential mapping and prove that the sub-Lorentzian distance is continuous for the mentioned structures. All presented results concerning reachable sets can be directly applied to generic control affine systems in \( {\mathbb{R}^3} \) with a scalar input u and constraints |u| ≤ δ.


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and ScienceCardinal Stefan Wyszyński UniversityWarsawPoland

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