This paper, proposes a complex Laplacian-based distributed control scheme for convergence in the multi-agent network. The proposed scheme has been designated as cascade formulation. The proposed technique exploits the traditional method of organizing large scattered networks into smaller interconnected clusters to optimize information flow within the network. The complex Laplacian-based approach results in a hierarchical structure, with the formation of a meta-cluster leading other clusters in the network. The proposed formulation enables flexibility to constrain the eigenspectra of the overall closed-loop dynamics, ensuring desired convergence rate and control input intensity. The sufficient conditions ensuring globally stable formation for the proposed formulation are also asserted. Robustness of the proposed formulation to uncertainties like loss in communication links and actuator failure have also been discussed. The effectiveness of the proposed approach is illustrated by simulating a finitely large network of 30 vehicles.

中文翻译：

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基于复杂拉普拉斯算子的多代理网络分布式控制

本文提出了一种复杂的基于拉普拉斯算子的分布式控制方案，用于在多智能体网络中收敛。提议的方案已被指定为级联公式。所提出的技术利用将大型分散网络组织成较小互连集群的传统方法来优化网络内的信息流。复杂的基于拉普拉斯算子的方法导致了层次结构，形成了一个引导网络中其他集群的元集群。所提出的公式能够灵活地约束整体闭环动力学的特征谱，确保所需的收敛速度和控制输入强度。还断言了确保所提出的配方的全局稳定形成的充分条件。还讨论了所提出的公式对通信链路丢失和执行器故障等不确定性的鲁棒性。通过模拟一个由 30 辆车组成的有限大型网络来说明所提出方法的有效性。