Soil searching by an artificial root
Analysis of PDEs
2020-05-14 v1 Optimization and Control
Abstract
We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a "breakdown configuration" is reached. Some numerical simulations are performed, to test the effectiveness of our feedback control algorithm.
Cite
@article{arxiv.2005.06069,
title = {Soil searching by an artificial root},
author = {Fabio Ancona and Alberto Bressan and Maria Teresa Chiri},
journal= {arXiv preprint arXiv:2005.06069},
year = {2020}
}
Comments
19 pages, 6 figures