Properties of the reachable set of control systems

We investigate some properties of the reachable set of a control system. Representing the system as a differential inclusion and using proximal Hamilton–Jacobi equation we describe its graph. We work in infinitely dimensional Hilbert space and use one sided Lipschitz approach. The funnel equation is considered in the last section. That equation describes the reachable set in arbitrary Banach space. We consider also the autonomous case and prove the existence of a limit of the reachable set.