吸引排斥作用下的网络化多智能体系统的群集行为研究

This proposal investigates collective behaviors of complex multi-agent systems in networks with attractive and repulsive interactions. For the case when the neighboring agents' relative information is available, simple criteria will be established for the linear multi-agent system reaching consensus with attractive and repulsive interactions. The convergence speed of the system will be analyzed. We will identify how to introduce the repulsive interaction to a network to accelerate the convergence of the system. For the case when the neighboring agents' absolute information is available, sufficient and necessary conditions will be proposed for the linear multi-agent system reaching consensus, realizing polarization, and clustering under a relaxed connectivity condition. The corresponding convergence speed will be analyzed. Finally, we will look into the impact of nonlinear coupling on collective behaviors of networked multi-agent systems. For the coupled nonlinear Kuramoto oscillator system, several typical coupling network topologies and general connected topologies will be studied and conditions will be established for frequency synchronization, phase synchronization, anti-phase synchronization and clustering for the system. This proposal will disclose the function of the repulsive interaction in the emergence of collective behaviors of multi-agent systems. The research results of the proposal will provide theoretical foundations for the design of new efficient and effective coordinated control algorithms for multi-agent systems.

本项目研究复杂多智能体系统在含有吸引排斥作用网络中的群集行为。针对吸引排斥作用下的网络，首先在邻居智能体相对信息可用时，建立线性多智能体系统状态达到一致的简易判别条件，分析系统的收敛速度，研究如何在网络中合理引入排斥作用加快系统的收敛速度；然后在邻居智能体绝对信息可用时，建立较宽松连通条件下线性多智能体系统达到一致、极化以及产生聚类的充分及必要条件，分析系统的收敛速度；最后讨论非线性耦合对网络化多智能体系统群集行为的影响，针对耦合非线性Kuramoto振子系统，研究几类典型耦合拓扑结构以及一般连通网络，建立系统频率同步、相位同步、反相位同步、聚类等的条件。本项目将揭示排斥作用在多智能体系统形成群集现象中的作用，项目成果将为设计新的快速有效的多智能体系统协调控制算法提供理论基础。

多智能体系统群集行为的研究是网络科学的一个热点问题，其研究成果为设计分布式协同控制算法提供指导。项目首先对邻居相对信息可用网络中的线性多智能体系统利用极限系统理论建立其指数一致性的条件，提出通过减小特定连边权重从而加快网络收敛速度的方法，提出随机采样下基于相对输出信息的一致性控制器设计方法，提出基于极限环的二维平面编队控制方法。对邻居绝对信息可用网络中的多智能体系统，建立随机矩阵乘积收敛的充分和必要条件，刻画其收敛速度，研究分布式协同算法异步实现的收敛性条件和通信延时对多智能体系统同步的影响。对非线性多智能体系统，建立系统状态达到一致、极化和聚类的条件。研究成果为从事多智能体系统协同控制研究的工程技术人员提供了一定的理论参考。

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