Birth of the shape of a reachable set
Alexander Ovseevich, Elena Goncharova
We address a linear control system under geometric constraints on control and study its reachable
sets starting at zero time from the origin. The main result is the existence of a limit shape of the
reachable sets as the terminal time tends to zero. Here, a shape of a set stands for the set
regarded up to an invertible linear transformation. Both autonomous and non-autonomous cases are
considered.