Optimization of a Perturbed Implicit Sweeping Process by Constrained Discontinuous Controls
Abstract
This paper studies optimal control problems governed by an implicit sweeping process with velocity-dependent constraint geometry, where the dynamics are described by a differential inclusion involving the normal cone to a moving convex polyhedral set. Such systems form a challenging class of nonsmooth differential inclusions due to the implicit coupling between the state, velocity, and constraint reaction. To address these difficulties, we use a method of discrete approximations together with tools of variational analysis and generalized differentiation. This approach allows us to derive necessary optimality conditions for local minimizer in discrete-time problems and subsequently pass to the limit to obtain optimality conditions for the original continuous-time system. The obtained results extend existing optimal control theory for sweeping processes to a class of implicit dynamical systems with state-and velocity-dependent constraints.
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BibTeX
@misc{dang2026optimization,
title = {{Optimization of a Perturbed Implicit Sweeping Process by Constrained Discontinuous Controls}},
author = {Yen Dang and Boris S. Mordukhovich and Dao Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21384},
eprint = {2610.21384},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21384},
}
RIS
TY - UNPB
TI - Optimization of a Perturbed Implicit Sweeping Process by Constrained Discontinuous Controls
AU - Yen Dang
AU - Boris S. Mordukhovich
AU - Dao Nguyen
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21384
UR - https://arxiv.org/abs/2610.21384
AB - This paper studies optimal control problems governed by an implicit sweeping process with velocity-dependent constraint geometry, where the dynamics are described by a differential inclusion involving the normal cone to a moving convex polyhedral set. Such systems form a challenging class of nonsmooth differential inclusions due to the implicit coupling between the state, velocity, and constraint reaction. To address these difficulties, we use a method of discrete approximations together with tools of variational analysis and generalized differentiation. This approach allows us to derive necessary optimality conditions for local minimizer in discrete-time problems and subsequently pass to the limit to obtain optimality conditions for the original continuous-time system. The obtained results extend existing optimal control theory for sweeping processes to a class of implicit dynamical systems with state-and velocity-dependent constraints.
ER -