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Adaptive time-delayed stabilization of steady states and periodic orbits. / Selivanov, A.; Lehnert, J.; Fradkov, A.; Schöll, E.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, No. 1, 2015, p. None.

Research output: Contribution to journal › Article

Harvard

Selivanov, A, Lehnert, J, Fradkov, A & Schöll, E 2015, 'Adaptive time-delayed stabilization of steady states and periodic orbits', Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, no. 1, pp. None. https://doi.org/10.1103/PhysRevE.91.012906

APA

Selivanov, A., Lehnert, J., Fradkov, A., & Schöll, E. (2015). Adaptive time-delayed stabilization of steady states and periodic orbits. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, (1), None. https://doi.org/10.1103/PhysRevE.91.012906

Vancouver

Selivanov A, Lehnert J, Fradkov A, Schöll E. Adaptive time-delayed stabilization of steady states and periodic orbits. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015;(1):None. https://doi.org/10.1103/PhysRevE.91.012906

Author

Selivanov, A. ; Lehnert, J. ; Fradkov, A. ; Schöll, E. / Adaptive time-delayed stabilization of steady states and periodic orbits. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015 ; No. 1. pp. None.

BibTeX

@article{ff2731c014134f009b23cfd1ed3e2625,
title = "Adaptive time-delayed stabilization of steady states and periodic orbits",
abstract = "{\textcopyright} 2015 American Physical Society.We derive adaptive time-delayed feedback controllers that stabilize fixed points and periodic orbits. First, we develop an adaptive controller for stabilization of a steady state by applying the speed-gradient method to an appropriate goal function and prove global asymptotic stability of the resulting system. For an example we show that the advantage of the adaptive controller over the nonadaptive one is in a smaller controller gain. Second, we propose adaptive time-delayed algorithms for stabilization of periodic orbits. Their efficiency is confirmed by local stability analysis. Numerical examples demonstrate the applicability of the proposed controllers.",
author = "A. Selivanov and J. Lehnert and A. Fradkov and E. Sch{\"o}ll",
year = "2015",
doi = "10.1103/PhysRevE.91.012906",
language = "English",
pages = "None",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Adaptive time-delayed stabilization of steady states and periodic orbits

AU - Selivanov, A.

AU - Lehnert, J.

AU - Fradkov, A.

AU - Schöll, E.

PY - 2015

Y1 - 2015

N2 - © 2015 American Physical Society.We derive adaptive time-delayed feedback controllers that stabilize fixed points and periodic orbits. First, we develop an adaptive controller for stabilization of a steady state by applying the speed-gradient method to an appropriate goal function and prove global asymptotic stability of the resulting system. For an example we show that the advantage of the adaptive controller over the nonadaptive one is in a smaller controller gain. Second, we propose adaptive time-delayed algorithms for stabilization of periodic orbits. Their efficiency is confirmed by local stability analysis. Numerical examples demonstrate the applicability of the proposed controllers.

AB - © 2015 American Physical Society.We derive adaptive time-delayed feedback controllers that stabilize fixed points and periodic orbits. First, we develop an adaptive controller for stabilization of a steady state by applying the speed-gradient method to an appropriate goal function and prove global asymptotic stability of the resulting system. For an example we show that the advantage of the adaptive controller over the nonadaptive one is in a smaller controller gain. Second, we propose adaptive time-delayed algorithms for stabilization of periodic orbits. Their efficiency is confirmed by local stability analysis. Numerical examples demonstrate the applicability of the proposed controllers.

U2 - 10.1103/PhysRevE.91.012906

DO - 10.1103/PhysRevE.91.012906

M3 - Article

SP - None

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

ER -

ID: 4014082