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Distributed optimization via active disturbance rejection control: A nabla fractional design
Kybernetika, Tome 60 (2024) no. 1, pp. 90-109 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.14736/kyb-2024-1-0090
Classification : 26A33, 49N15, 68W15, 93D05, 93D21
Keywords: distributed optimization; nabla fractional difference; active disturbance rejection control; Lyapunov method 
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     title = {Distributed optimization via active disturbance rejection control: {A} nabla fractional design},
     journal = {Kybernetika},
     pages = {90--109},
     year = {2024},
     volume = {60},
     number = {1},
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     zbl = {07893449},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2024-1-0090/}
}
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Zeng, Yikun; Wei, Yiheng; Zhou, Shuaiyu; Yue, Dongdong. Distributed optimization via active disturbance rejection control: A nabla fractional design. Kybernetika, Tome 60 (2024) no. 1, pp. 90-109. doi: 10.14736/kyb-2024-1-0090

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