Bibliografie

Journal Article

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

Colombo G., Gidoni Paolo, Vilches E.

: Discrete and Continuous Dynamical Systems vol.42, 2 (2022), p. 737-757

: GF19-29646L, GA ČR

: sweeping process, running-periodic solutions, relative-periodic solutions, asymptotic stability, crawling locomotion

: 10.3934/dcds.2021135

: http://library.utia.cas.cz/separaty/2022/MTR/gidoni-0552385.pdf

: https://www.aimsciences.org/article/doi/10.3934/dcds.2021135

(eng): 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.

: BA

: 10102