Geodesic
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

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In this paper we investigate analytic affine control systems q ˙ 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.

DOI : 10.1051/cocv/2011202
Classification : 53B30, 34H05, 49K99
Keywords: sub-lorentzian manifolds, geodesics, reachable sets, geometric optimality, affine control systems 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv/2011202/}
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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

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