TY - JOUR
T1 - Regularity properties of optimal trajectories of single-input control systems in dimension three
JF - Journal of Mathematical Sciences 126 (2005) 1561-1573
Y1 - 2005
A1 - Mario Sigalotti
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/4794
U1 - 4564
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -