Geometry of neighborhoods of singular trajectories in problems with multidimensional control (Q742248)

Finite-dimensional optimal control problems for smooth control systems are considered with multidimensional control. An extension of the order of a singular trajectory is defined and described by a flag of linear subspaces in the control space. In this way, for affine control systems, necessary conditions are obtained on the junction of a nonsingular trajectory with a singular one. A class of problems is studied where the junction of singular optimal trajectories with nonsingular ones leads to irrational winding of a torus.