Constructing Reachable Sets for a Class of Nonsmooth Control Systems on a Plane

A way of determining the approximate boundary of a reachable set is proposed for a class of nonsmooth controlled dynamic systems on a plane in economics. The technique is based on an explicit procedure for smoothing the system and using the apparatus of Pontryagin’s maximum principle. As an example, the problem is posed of constructing the boundary of the reachable set for a controlled version of the well-known Kaldor business cycle model.