Consensus Tracking of Fractional-Order Multiagent Systems via Fractional-Order Iterative Learning Control

In this work, the consensus problem of fractional-order multiagent systems with the general linear model of fixed topology is studied. Both distributed PDα-type and Dα-type fractional-order iterative learning control (FOILC) algorithms are proposed. Here, a virtual leader is introduced to generate the desired trajectory, fixed communication topology is considered, and only a subset of followers can access the desired trajectory. The convergence conditions are proved using graph theory, fractional calculus, and λ norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both PDα-type and Dα-type FOILC algorithms. Extensive numerical simulations are given to demonstrate the feasibility and effectiveness.