Kybernetika 60 no. 1, 90-109, 2024

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

Yikun Zeng, Yiheng Wei, Shuaiyu Zhou and Dongdong YueDOI: 10.14736/kyb-2024-1-0090

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.

Keywords:

distributed optimization, Lyapunov method, nabla fractional difference, active disturbance rejection control

Classification:

68W15, 26A33, 93D05, 93D21, 49N15

paper.pdf

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