Published Paper
Inserted: 13 may 2020
Last Updated: 4 jan 2024
Journal: SIAM Journal on Applied Mathematics
Year: 2022
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.
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