The structure of reachable sets for affine control systems induced by generalized Martinet sub-Lorentzian metrics
Cardinal Stefan Wyszyński University, Faculty of Mathematics and
Natural Sciences Cardinal Stefan Wyszyński, University Dewajtis 5,
2 Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
In this paper we investigate analytic affine control systems = 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.
Mathematics Subject Classification: 53B30 / 34H05 / 49K99
Key words: Sub-Lorentzian manifolds / geodesics / reachable sets / geometric optimality / affine control systems
© EDP Sciences, SMAI, 2012