Observation stability and convergence for neural-type evolutionary variational inequalities

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Observation stability and convergence for neural-type evolutionary variational inequalities. / Reitmann, Stefan; Jung, Bernhard; Kudryashova, Elena V.; Reitmann, Volker.

In: Differencialnie Uravnenia i Protsesy Upravlenia, Vol. 2021, No. 2, 2021, p. 126-155.

Research output: Contribution to journal › Article › peer-review

Author

Reitmann, Stefan ; Jung, Bernhard ; Kudryashova, Elena V. ; Reitmann, Volker. / Observation stability and convergence for neural-type evolutionary variational inequalities. In: Differencialnie Uravnenia i Protsesy Upravlenia. 2021 ; Vol. 2021, No. 2. pp. 126-155.

BibTeX

@article{67a0c6416a6a4846b9da7afcede1165b,

title = "Observation stability and convergence for neural-type evolutionary variational inequalities",

abstract = "We derive absolute observation stability and instability results for controlled evolutionary inequalities which are based on frequency-domain characteristics of the linear part of the inequalities.The uncertainty parts of the inequalities (nonlinearities which represent external forces and constitutive laws) are described by certain local and integral quadratic constraints. Other terms in the considered evolutionary inequalities represent contact-type properties of a mechanical system with dry friction. The absolute stability criteria with respect to a class of observation operators (or measurement operators) gives the opportunity to prove the weak convergence of arbitrary solutions of inequalities to their stationary sets. In particular the obtained results can be used for the investigation of continuum type memories in neural networks. In such a way we can introduce a new type of neurons with hysteretic nonlinearities which are described by evolutionary variational inequalities.",

keywords = "Absolute observation stability, Evolutionary variational inequalities, Frequency-domain conditions, Hysteretic neural networks",

author = "Stefan Reitmann and Bernhard Jung and Kudryashova, {Elena V.} and Volker Reitmann",

year = "2021",

language = "English",

volume = "2021",

pages = "126--155",

journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1817-2172",

publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",

number = "2",

}

RIS

TY - JOUR

T1 - Observation stability and convergence for neural-type evolutionary variational inequalities

AU - Reitmann, Stefan

AU - Jung, Bernhard

AU - Kudryashova, Elena V.

AU - Reitmann, Volker

PY - 2021

Y1 - 2021

N2 - We derive absolute observation stability and instability results for controlled evolutionary inequalities which are based on frequency-domain characteristics of the linear part of the inequalities.The uncertainty parts of the inequalities (nonlinearities which represent external forces and constitutive laws) are described by certain local and integral quadratic constraints. Other terms in the considered evolutionary inequalities represent contact-type properties of a mechanical system with dry friction. The absolute stability criteria with respect to a class of observation operators (or measurement operators) gives the opportunity to prove the weak convergence of arbitrary solutions of inequalities to their stationary sets. In particular the obtained results can be used for the investigation of continuum type memories in neural networks. In such a way we can introduce a new type of neurons with hysteretic nonlinearities which are described by evolutionary variational inequalities.

AB - We derive absolute observation stability and instability results for controlled evolutionary inequalities which are based on frequency-domain characteristics of the linear part of the inequalities.The uncertainty parts of the inequalities (nonlinearities which represent external forces and constitutive laws) are described by certain local and integral quadratic constraints. Other terms in the considered evolutionary inequalities represent contact-type properties of a mechanical system with dry friction. The absolute stability criteria with respect to a class of observation operators (or measurement operators) gives the opportunity to prove the weak convergence of arbitrary solutions of inequalities to their stationary sets. In particular the obtained results can be used for the investigation of continuum type memories in neural networks. In such a way we can introduce a new type of neurons with hysteretic nonlinearities which are described by evolutionary variational inequalities.

KW - Absolute observation stability

KW - Evolutionary variational inequalities

KW - Frequency-domain conditions

KW - Hysteretic neural networks

UR - http://www.scopus.com/inward/record.url?scp=85114155606&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85114155606

VL - 2021

SP - 126

EP - 155

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 2

ER -

ID: 86422094