# The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 4, page 1150-1177
- ISSN: 1292-8119

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topGrochowski, Marek. "The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics." ESAIM: Control, Optimisation and Calculus of Variations 18.4 (2012): 1150-1177. <http://eudml.org/doc/272887>.

@article{Grochowski2012,

abstract = {In this paper we investigate analytic affine control systems $\dot\{q\}$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.},

author = {Grochowski, Marek},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {sub-lorentzian manifolds; geodesics; reachable sets; geometric optimality; affine control systems; sub-Lorentzian manifolds},

language = {eng},

number = {4},

pages = {1150-1177},

publisher = {EDP-Sciences},

title = {The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics},

url = {http://eudml.org/doc/272887},

volume = {18},

year = {2012},

}

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

PB - EDP-Sciences

VL - 18

IS - 4

SP - 1150

EP - 1177

AB - In this paper we investigate analytic affine control systems $\dot{q}$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.

LA - eng

KW - sub-lorentzian manifolds; geodesics; reachable sets; geometric optimality; affine control systems; sub-Lorentzian manifolds

UR - http://eudml.org/doc/272887

ER -

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