Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions

This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis truncated Hausdorff distances between polyhedra, we derive new existence and uniqueness theorems for trajectories corresponding various classes control functions acting sets. Then establish quantitative stability results, which provide efficient estimates trajectory dependence controls initial values. Our final topic, accomplished finite-dimensional state spaces, deriving necessary optimality suboptimality conditions systems endpoint constrains by using constructive discrete approximations.