Standard

The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well. / Akhmetzhanov, A. R.; Melikyan, A. A.; Fradkov, A. L.

в: Journal of Applied Mathematics and Mechanics, Том 71, № 6, 2007, стр. 809-818.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Akhmetzhanov, AR, Melikyan, AA & Fradkov, AL 2007, 'The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well', Journal of Applied Mathematics and Mechanics, Том. 71, № 6, стр. 809-818. https://doi.org/10.1016/j.jappmathmech.2007.12.001

APA

Akhmetzhanov, A. R., Melikyan, A. A., & Fradkov, A. L. (2007). The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well. Journal of Applied Mathematics and Mechanics, 71(6), 809-818. https://doi.org/10.1016/j.jappmathmech.2007.12.001

Vancouver

Akhmetzhanov AR, Melikyan AA, Fradkov AL. The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well. Journal of Applied Mathematics and Mechanics. 2007;71(6):809-818. https://doi.org/10.1016/j.jappmathmech.2007.12.001

Author

Akhmetzhanov, A. R. ; Melikyan, A. A. ; Fradkov, A. L. / The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well. в: Journal of Applied Mathematics and Mechanics. 2007 ; Том 71, № 6. стр. 809-818.

BibTeX

@article{838a4413b26046b59c1505aa21ba1324,
title = "The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well",
abstract = "The problem of controlling the escape of a particle from a potential well for a nonlinear system with friction is considered. The velocity-gradient method [Polushin IG, Fradkov AL, Hill, D. Passivity and passivation in non-linear systems. Avtomatika i Telemekhanika 2000;3:3-37] is proved to be optimal in the sense that if it does not guarantee escape from the well, then this is also impossible with any other control law. Nonlinear Duffing and Helmholtz oscillators with one degree of freedom and negative stiffness are considered. For each of them a curve is constructed separating the parameter plane of the problem into two parts: one where escape is feasible and one where it is not. An estimate is obtained for the inclination angle of the tangent to that curve near the origin.",
author = "Akhmetzhanov, {A. R.} and Melikyan, {A. A.} and Fradkov, {A. L.}",
year = "2007",
doi = "10.1016/j.jappmathmech.2007.12.001",
language = "English",
volume = "71",
pages = "809--818",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "6",

}

RIS

TY - JOUR

T1 - The optimality of the velocity-gradient method in the problem of controlling the escape from a potential well

AU - Akhmetzhanov, A. R.

AU - Melikyan, A. A.

AU - Fradkov, A. L.

PY - 2007

Y1 - 2007

N2 - The problem of controlling the escape of a particle from a potential well for a nonlinear system with friction is considered. The velocity-gradient method [Polushin IG, Fradkov AL, Hill, D. Passivity and passivation in non-linear systems. Avtomatika i Telemekhanika 2000;3:3-37] is proved to be optimal in the sense that if it does not guarantee escape from the well, then this is also impossible with any other control law. Nonlinear Duffing and Helmholtz oscillators with one degree of freedom and negative stiffness are considered. For each of them a curve is constructed separating the parameter plane of the problem into two parts: one where escape is feasible and one where it is not. An estimate is obtained for the inclination angle of the tangent to that curve near the origin.

AB - The problem of controlling the escape of a particle from a potential well for a nonlinear system with friction is considered. The velocity-gradient method [Polushin IG, Fradkov AL, Hill, D. Passivity and passivation in non-linear systems. Avtomatika i Telemekhanika 2000;3:3-37] is proved to be optimal in the sense that if it does not guarantee escape from the well, then this is also impossible with any other control law. Nonlinear Duffing and Helmholtz oscillators with one degree of freedom and negative stiffness are considered. For each of them a curve is constructed separating the parameter plane of the problem into two parts: one where escape is feasible and one where it is not. An estimate is obtained for the inclination angle of the tangent to that curve near the origin.

UR - http://www.scopus.com/inward/record.url?scp=40249100137&partnerID=8YFLogxK

U2 - 10.1016/j.jappmathmech.2007.12.001

DO - 10.1016/j.jappmathmech.2007.12.001

M3 - Article

AN - SCOPUS:40249100137

VL - 71

SP - 809

EP - 818

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 6

ER -

ID: 87382592