Existence results for sweeping process with almost convex perturbation

We consider an evolution inclusion governed by the so-called “sweeping process”. The right-hand side contains a set-valued perturbation, upper semi-continuous with nonempty compact and almost convex values. We generalize first an existence result when the perturbation is with convex but not necessary bounded values, topological properties of the attainable set are also established. Then, in a particular case arising in planning procedures, the problem with almost convex perturbation is investigated in order to establish the existence of time optimal solutions.