Abstract
Let M be a σ-compact C∞ manifold of dimension d ≥ 3. Consider on M a single-input control system : x˙(t)=G0(x(t))+u(t)F1(x(t)), where F0, F1 are C∞ vector fields on M and the set of admissible controls U is the set of bounded measurable mappings u : [0Tu]↦R, Tu > 0. A singular trajectory is an output corresponding to a control such that the differential of the input-output mapping is not of maximal rank. In this article we show that for an open dense subset of the set of pairs of vector fields (F0, F1), endowed with the C∞-Whitney topology, all the singular trajectories are with minimal order and the corank of the singularity is one.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.