Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph