Nabla fractional distributed optimization algorithms over undirected/directed graphs

Hong, Xiaolin; Wei, Yiheng; Zhou, Shuaiyu; Yue, Dongdong

doi:10.1016/j.jfranklin.2024.01.013

Cited by 1 publication

(1 citation statement)

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“…However, these studies primarily center on continuoustime algorithms, potentially bringing about increased computational complexity and communication costs. Then, [11,12] extended the objective function to general convex functions or strongly convex functions and designed nabla fractional distributed optimization algorithms for different kinds of graphs. Through these studies, it is found that fractional calculus can improve the performance of optimization algorithm, and its non-Markov property can make reasonable use of the past information and avoid the real-time calculation of gradient.…”

Section: Introductionmentioning

confidence: 99%

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

Zeng,

Wei,

Zhou

et al. 2024

Kybernetika

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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.

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Section: Introductionmentioning

confidence: 99%