Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

0552385 - ÚTIA 2022 RIV US eng J - Journal Article
Colombo, G. - Gidoni, Paolo - Vilches, E.
Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction.
Discrete and Continuous Dynamical Systems. Roč. 42, č. 2 (2022), s. 737-757. ISSN 1078-0947. E-ISSN 1553-5231
R&D Projects: GA ČR(CZ) GF19-29646L
Institutional support: RVO:67985556
Keywords : sweeping process * running-periodic solutions * relative-periodic solutions * asymptotic stability * crawling locomotion
OECD category: Applied mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2022/MTR/gidoni-0552385.pdf https://www.aimsciences.org/article/doi/10.3934/dcds.2021135

We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger W1,2 convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only convergence.
Permanent Link: http://hdl.handle.net/11104/0327549