Differentiability and Control of a Model for Granular Material Accumulation
Optimization and Control
2021-06-25 v1
Abstract
We consider differentiability issues associated to the problem of minimizing the accumulation of a granular cohesionless material on a certain surface. The design variable or control is determined by source locations and intensity thereof. The control problem is described by an optimization problem in function space and constrained by a variational inequality or a non-smooth equation. We address a regularization approach via a family of nonlinear partial differential equations, and provide a novel result of Newton differentiability of the control-to-state map. Further, we discuss solution algorithms for the state equation as well as for the optimization problem.
Cite
@article{arxiv.2106.12653,
title = {Differentiability and Control of a Model for Granular Material Accumulation},
author = {Rafael Arndt and Carlos N. Rautenberg},
journal= {arXiv preprint arXiv:2106.12653},
year = {2021}
}