This study focuses on implementing consensus tracking using both open-loop and closed-loop Dα-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.

中文翻译：

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具有状态延迟的分数阶线性多智能体系统的开环和闭环Dα型迭代学习控制

这项研究的重点是针对具有状态延迟的分数阶多智能体系统（FOMAS），使用开环和闭环Dα型迭代学习控制（ILC）方案实施共识跟踪。通过引入虚拟领导者来构建期望的轨迹，并考虑固定的通信拓扑，只有跟随者的子集可以访问期望的轨迹。对于每种控制方案，分别为一个代理设计一个控制器。根据业务代表与虚拟领导者之间的跟踪误差以及业务代表与相邻智能代理之间在上一次迭代（对于开环方案）或当前运行期间（对于闭环方案）的跟踪误差，每个控制器通过拓扑中的通信权重的组合不断地校正最后的控制律，以获得理想的控制律。通过严格的分析，为两种控制方案建立了充分的条件，以确保所有代理都可以在有限的时间间隔内沿迭代轴获得渐近一致的输出。足够的数值仿真结果证明了该控制方案的有效性，并提供了一些有意义的比较结果。