Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems

0558112 - MÚ 2023 RIV US eng J - Journal Article
Gudoshnikov, Ivan - Makarenkov, O. - Rachinskii, D.
Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems.
SIAM Journal on Control and Optimization. Roč. 60, č. 3 (2022), s. 1320-1346. ISSN 0363-0129. E-ISSN 1095-7138
R&D Projects: GA ČR(CZ) GA20-14736S
Grant - others:AV ČR(CZ) L100192151
Institutional support: RVO:67985840
Keywords : finite-time stability * Lyapunov function * normal cone * polyhedral constraint
OECD category: Pure mathematics
Impact factor: 2.2, year: 2022
Method of publishing: Limited access
https://doi.org/10.1137/20M1388796

We use the ideas of Adly, Attouch, and Cabot [in Nonsmooth Mechanics and Analysis, Adv. Mech. Math. 12, Springer, New York, 2006, pp. 289-304] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form C + c(t). We then employ the ideas of Moreau [in New Variational Techniques in Mathematical Physics (Centro Internaz. Mat. Estivo (CIME), II Ciclo, Bressanone, 1973), Edizioni Cremonese, Rome, 1974, pp. 171-322] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex “A” or the active face “A” of the polyhedron that the vector c(t) points at, (ii) computing the distance from c(t) to the normal cone to the polyhedron at “A.” We provide a computational guide for solving problems (i)-(ii) in the case of an arbitrary elastoplastic system and apply it to a particular example. Due to the simplicity of the particular example, we can solve (i)-(ii) by the methods of linear algebra and basic combinatorics.
Permanent Link: http://hdl.handle.net/11104/0331911