%0 Journal Article
%J Journal of Mathematical Sciences 126 (2005) 1561-1573
%D 2005
%T Regularity properties of optimal trajectories of single-input control systems in dimension three
%A Mario Sigalotti
%X Let q=f(q)+ug(q) be a smooth control system on a three-dimensional manifold. Given a point q 0 of the manifold at which the iterated Lie brackets of f and g satisfy some prescribed independence condition, we analyze the structure of a control function u(t) corresponding to a time-optimal trajectory lying in a neighborhood of q 0. The control turns out to be the concatenation of some bang-bang and some singular arcs. More general optimality criteria than time-optimality are considered. The paper is a step toward to the analysis of generic single-input systems affine in the control in dimension 3. The main techniques used are second-order optimality conditions and, in particular, the index of the second variation of the switching times for bang-bang trajectories.
%B Journal of Mathematical Sciences 126 (2005) 1561-1573
%I Springer
%G en
%U http://hdl.handle.net/1963/4794
%1 4564
%2 Mathematics
%3 Functional Analysis and Applications
%4 -1
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-17T08:06:19Z\\nNo. of bitstreams: 1\\nsuz.pdf: 199707 bytes, checksum: 1d18998eb7281177da4a442135d9b77d (MD5)
%R 10.1007/s10958-005-0044-z