Relaxed control

Summary

A relaxed control assigns to each time a probability measure on the set of control values, instead of a single control value. The system then moves with the average of the velocities with respect to this measure. Relaxed controls fill in the convex hulls of the velocity sets, so optimal control problems without a minimizer gain one in the relaxed sense. They are the control theory counterpart of Young measures and of the relaxation of a variational problem.