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.
distributed optimization, Lyapunov method, nabla fractional difference, active disturbance rejection control
68W15, 26A33, 93D05, 93D21, 49N15