Distributed optimization via active disturbance rejection control: A nabla fractional design

Yikun Zeng; Yiheng Wei; Shuaiyu Zhou; Dongdong Yue

Kybernetika (2024)

  • Issue: 1, page 90-109
  • ISSN: 0023-5954

Abstract

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This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal solution when the external disturbance is bounded. In particular, for constant disturbances, the Frac-ESO is Mittag-Leffler convergent and the optimization problem can be solved exactly. Finally, numerical simulations are presented to validate the effective properties of the proposed algorithm.

How to cite

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Zeng, Yikun, et al. "Distributed optimization via active disturbance rejection control: A nabla fractional design." Kybernetika (2024): 90-109. <http://eudml.org/doc/299548>.

@article{Zeng2024,
abstract = {This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal solution when the external disturbance is bounded. In particular, for constant disturbances, the Frac-ESO is Mittag-Leffler convergent and the optimization problem can be solved exactly. Finally, numerical simulations are presented to validate the effective properties of the proposed algorithm.},
author = {Zeng, Yikun, Wei, Yiheng, Zhou, Shuaiyu, Yue, Dongdong},
journal = {Kybernetika},
keywords = {distributed optimization; nabla fractional difference; active disturbance rejection control; Lyapunov method},
language = {eng},
number = {1},
pages = {90-109},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Distributed optimization via active disturbance rejection control: A nabla fractional design},
url = {http://eudml.org/doc/299548},
year = {2024},
}

TY - JOUR
AU - Zeng, Yikun
AU - Wei, Yiheng
AU - Zhou, Shuaiyu
AU - Yue, Dongdong
TI - Distributed optimization via active disturbance rejection control: A nabla fractional design
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
IS - 1
SP - 90
EP - 109
AB - This paper studies distributed optimization problems of a class of agents with fractional order dynamics and unknown external disturbances. Motivated by the celebrated active disturbance rejection control (ADRC) method, a fractional order extended state observer (Frac-ESO) is first constructed, and an ADRC-based PI-like protocol is then proposed for the target distributed optimization problem. It is rigorously shown that the decision variables of the agents reach a domain of the optimal solution when the external disturbance is bounded. In particular, for constant disturbances, the Frac-ESO is Mittag-Leffler convergent and the optimization problem can be solved exactly. Finally, numerical simulations are presented to validate the effective properties of the proposed algorithm.
LA - eng
KW - distributed optimization; nabla fractional difference; active disturbance rejection control; Lyapunov method
UR - http://eudml.org/doc/299548
ER -

References

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