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