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This paper investigates the robust consensus tracking problem of fractional-order multi-agent systems (FOMASs) subject to the iteration-varying initial state shifts. For the FOMASs including one leader agent and multiple follower agents, the PD $^{\alpha }$ -type ILC protocol with the rectifying action is proposed. By improving the existing average operator and choosing the suitable variables, the leader-following FOMASs under the proposed protocol are rewritten as a two-dimensional (2D) dynamical model. Based on the 2D analysis approach, the sufficient conditions are presented for the consensus of FOMASs. It is shown that due to the improved average operator, the derived sufficient conditions are more relaxed. With the increase of iteration step, the output of each follower agent will converge, and as the iteration step goes to infinity, and the limit output of each follower agent can be formulated in terms of the output of leader agent, the mean values of the initial output tracking errors, the learning gain matrices, the fractional order and the structure of communication graph. Finally, two numerical simulation examples are presented to demonstrate the effectiveness of the proposed method.

Iterative Learning Consensus of Fractional-Order Multi-Agent Systems Subject to Iteration-Varying Initial State Shifts