Existence of optimal solutions and necessary optimality conditions for a controlled version of Moreau's sweeping process are derived. The control is a measurable ingredient of the dynamics and the constraint set is a polyhedron. The novelty consists in considering time periodic trajectories, adding the requirement that the control have zero average, and considering an integral functional that lacks weak semicontinuity. A model coming from the locomotion of a soft-robotic crawler, that motivated our setting, is analysed in detail. In obtaining necessary conditions, an improvement of the method of discrete approximations is used.
@article{arxiv.2002.08395,
title = {On the optimal control of rate-independent soft crawlers},
author = {Giovanni Colombo and Paolo Gidoni},
journal= {arXiv preprint arXiv:2002.08395},
year = {2022}
}