| Issue |
ESAIM: COCV
Volume 18, Number 4, October-December 2012
|
|
|---|---|---|
| Page(s) | 1150 - 1177 | |
| DOI | https://doi.org/10.1051/cocv/2011202 | |
| Published online | 16 January 2012 | |
The structure of reachable sets for affine control systems induced by generalized Martinet sub-Lorentzian metrics
1
Cardinal Stefan Wyszyński University, Faculty of Mathematics and
Natural Sciences Cardinal Stefan Wyszyński, University Dewajtis 5,
01-815
Warszawa,
Poland
m.grochowski@uksw.edu.pl
2
Institute of Mathematics, Polish Academy of
Sciences, ul. Śniadeckich
8, 00-950
Warszawa,
Poland
Received:
13
June
2011
In this paper we investigate analytic affine control systems 
= X + uY, u ∈ [a,b] , where
X,Y is an orthonormal frame for a generalized Martinet sub-Lorentzian
structure of order k of Hamiltonian type. We construct normal forms for
such systems and, among other things, we study the connection between the presence of the
singular trajectory starting at q0 on the boundary of the
reachable set from q0 with the minimal number of analytic
functions needed for describing the reachable set from q0.
Mathematics Subject Classification: 53B30 / 34H05 / 49K99
Key words: Sub-Lorentzian manifolds / geodesics / reachable sets / geometric optimality / affine control systems
© EDP Sciences, SMAI, 2012
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