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The structure of reachable sets for affine control systemsinduced by generalized Martinet sub-Lorentzian metrics

Published online by Cambridge University Press:  16 January 2012

Marek Grochowski
Marek Grochowski*
Affiliation:
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 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
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Abstract

In this paper we investigate analytic affine control systems \hbox{$\dot{q}$}q̇ = X + uY, u ∈  [a,b] , whereX,Y is an orthonormal frame for a generalized Martinet sub-Lorentzianstructure of order k of Hamiltonian type. We construct normal forms forsuch systems and, among other things, we study the connection between the presence of thesingular trajectory starting at q0 on the boundary of thereachable set from q0 with the minimal number of analyticfunctions needed for describing the reachable set from q0.

Keywords

Sub-Lorentzian manifoldsgeodesicsreachable setsgeometric optimalityaffine control systems
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1150 - 1177
Copyright
© EDP Sciences, SMAI, 2012

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