On the time optimization problem for two-dimensional control systems

We consider a time optimization problem for two-dimensional nonlinear control systems. For a constraint for the control vector u we take a convex polygon U. We obtain effective sufficient conditions under which the time-optimal control is equivalent in the Lebesgue sense to a piecewise constant control that has finitely many points of discontinuity and ranges in the set of vertices of U. We give examples illustrating the results.