@article {2005,
title = {Regularity properties of optimal trajectories of single-input control systems in dimension three},
journal = {Journal of Mathematical Sciences 126 (2005) 1561-1573},
year = {2005},
publisher = {Springer},
abstract = {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.},
doi = {10.1007/s10958-005-0044-z},
url = {http://hdl.handle.net/1963/4794},
author = {Mario Sigalotti}
}