Mathematics

In the talk it is analized the structure of a control function u(t) corresponding to an optimal trajectory for the system \dot{q}=f(q)+ug(q) in R^3 nearby a point where some nondegenericity conditions are satisfied. As we will see the control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by six.