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

Marek Grochowski

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

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

Abstract

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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.

How to cite

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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 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 -

References

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