In this paper we investigate analytic affine control systems q̇ = 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.
Mots clés : sub-lorentzian manifolds, geodesics, reachable sets, geometric optimality, affine control systems
@article{COCV_2012__18_4_1150_0,
author = {Grochowski, Marek},
title = {The structure of reachable sets for affine control systems induced by generalized {Martinet} sub-lorentzian metrics},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1150--1177},
publisher = {EDP-Sciences},
volume = {18},
number = {4},
year = {2012},
doi = {10.1051/cocv/2011202},
mrnumber = {3019476},
zbl = {1268.53040},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2011202/}
}
TY - JOUR AU - Grochowski, Marek TI - The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 1150 EP - 1177 VL - 18 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011202/ DO - 10.1051/cocv/2011202 LA - en ID - COCV_2012__18_4_1150_0 ER -
%0 Journal Article %A Grochowski, Marek %T The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 1150-1177 %V 18 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011202/ %R 10.1051/cocv/2011202 %G en %F COCV_2012__18_4_1150_0
Grochowski, Marek. The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1150-1177. doi : 10.1051/cocv/2011202. http://www.numdam.org/articles/10.1051/cocv/2011202/
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