Consistent approximations of the zeno behaviour in affine-type switched dynamic systems

Vadim Azhmyakov

Resultado de la investigación: Contribución a una revistaArtículo

1 Cita (Scopus)

Resumen

Copyright © 2016 Vadim Azhmyakov. This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour.We also discuss shortly some possible applications of the proposed approximation schemes.
Idioma originalInglés estadounidense
Páginas (desde-hasta)1 - 9, 
PublicaciónAbstract and Applied Analysis
Volumen2016
N.ºID 2091526
DOI
EstadoPublicada - 1 ene 2016

Huella dactilar

Switched Systems
Dynamic Systems
Dynamical systems
Approximation
Control System
Variational techniques
Affine Structure
Control systems
Discrete Dynamics
Systems Engineering
Approximation Scheme
Systems engineering
Dynamic models
Dynamic Model
Trajectories
Projection
Mathematical Model
Trajectory
Mathematical models
Interval

Citar esto

@article{05040c042edb44fc946ecf915d6e372b,
title = "Consistent approximations of the zeno behaviour in affine-type switched dynamic systems",
abstract = "Copyright {\circledC} 2016 Vadim Azhmyakov. This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour.We also discuss shortly some possible applications of the proposed approximation schemes.",
author = "Vadim Azhmyakov",
year = "2016",
month = "1",
day = "1",
doi = "10.1155/2016/2091526",
language = "American English",
volume = "2016",
pages = "1 -- 9, ",
journal = "Abstract and Applied Analysis",
issn = "1085-3375",
publisher = "Hindawi Publishing Corporation",
number = "ID 2091526",

}

Consistent approximations of the zeno behaviour in affine-type switched dynamic systems. / Azhmyakov, Vadim.

En: Abstract and Applied Analysis, Vol. 2016, N.º ID 2091526, 01.01.2016, p. 1 - 9, .

Resultado de la investigación: Contribución a una revistaArtículo

TY - JOUR

T1 - Consistent approximations of the zeno behaviour in affine-type switched dynamic systems

AU - Azhmyakov, Vadim

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Copyright © 2016 Vadim Azhmyakov. This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour.We also discuss shortly some possible applications of the proposed approximation schemes.

AB - Copyright © 2016 Vadim Azhmyakov. This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the corresponding behaviour, mathematical models of many engineering systems may be Zeno due to the used formal abstraction. We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. A generic trajectory associated with the Zeno dynamics can finally be characterized as a result of a specific projection or/and an optimization procedure applied to the original dynamic model. The obtained analytic and variational techniques provide an effective methodology for constructive approximations of the general Zeno-type behaviour.We also discuss shortly some possible applications of the proposed approximation schemes.

U2 - 10.1155/2016/2091526

DO - 10.1155/2016/2091526

M3 - Article

VL - 2016

SP - 1 - 9, 

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

SN - 1085-3375

IS - ID 2091526

ER -