Consensus Control of Fractional-Order Multi-Agent Systems With Time Delays via Fractional-Order Iterative Learning Control

This paper considers the leader-following consensus tracking problem of fractional-order multi-agent systems (FOMASs) that contain communication time delays. By combining the iterative learning control (ILC) approach and fractional-order calculus, a distributed $PD^{\alpha }$ -type fractional-order iterative learning control (FOILC) and a distributed $D^{\alpha }$ -type FOILC algorithm are proposed, respectively. Based on graph theory and $\lambda $ -norm theory, the consensus problems of the proposed algorithms are discussed, and their convergence conditions are identified. The theoretical analysis demonstrates that as the number of iterations increases, all fractional-order agents with communication time delays can realize consensus exactly on the desired output trajectory by selecting suitable gain matrices of FOILC over a finite time interval. Illustrative examples are presented, on which the performances of the proposed method are evaluated.