Open-loop and closed-loop Dα-type iterative learning control for fractional-order linear multi-agent systems with state-delays

This study focuses on implementing consensus tracking using both open-loop and closed-loop -type iterative learning control (ILC) schemes, for fractional-order multi-agent systems (FOMASs) with state-delays.The desired trajectory is constructed by introducing a virtual leader, and the fixed communication topology is considered and only a subset of followers can access the desired trajectory.For each control scheme, one controller is designed for one agent individually.According to the tracking error between the agent and the virtual leader, and the tracking errors between the agent and neighboring agents during the last iteration (for open-loop scheme) or the current running (for closed-loop scheme), each controller continuously corrects the last control law by a combination of communication weights in the topology to obtain the ideal control law.Through the rigorous analysis, sufficient conditions for both control schemes are established to ensure that all agents can achieve the asymptotically consistent output along the iteration axis within a finite-time interval.Sufficient numerical simulation results demonstrate the effectiveness of the control schemes, and provide some meaningful comparison results.