第三章 多智能体系统通信拓扑最优设计.PDF

第33 卷第2 期 控制 理 论 与 应 用 Vol. 33 No. 2 2016 年2 月 Control Theory Applications Feb. 2016 DOI: 10.7641/CTA.2016.50468 多多多智智智能能能体体体系系系统统统通通通信信信拓拓拓扑扑扑最最最优优优设设设计计计 袁玩贵 , 屈百达 (1. 江南大学理学院, 江苏无锡214122; 2. 江南大学物联网学院, 江苏无锡214122) 摘要: 运用控制理论, 矩阵论及最小二乘等理论, 研究了多智能体系统的分组一致性与系统通信拓扑图的拉普拉 斯矩阵属于特征值的特征向量之间的关系. 给出了在线性协议控制下, 系统达到一致性和分组一致性, 其通信拓扑 的设计方法. 提出了一阶多智能体系统的总能量概念, 并得到了系统在能量最省时通信拓扑的最优设计. 仿真实例 佐证本文主要结论的正确性. 关键词: 多智能体系统; 一致性; 分组一致性; 通信拓扑; 系统能量; 最优设计 中图分类号: TP273 文献标识码: A The optimal design for interaction topology of multi-agent systems YUAN Wan-gui, QU Bai-da (1. School of Science, Jiangnan University, Wuxi Jangsu 214122, China; 2. School of Internet of Things Engineering, Jiangnan University, Wuxi Jangsu 214122, China) Abstract: Based on graph theory, matrix theory and least square theory, the relationship is studied between the group consistency and the eigenvectors of Laplacian matrix associated with eigenvalue for multi-agent systems. To obtain the consensus or group consistency, a design method for unidirectional information exchange topologies is provided based on the linear control protocol. The total energy is defined about the one-order multi-agent systems. And a optimal design is proposed so that the system energy is minimum. Simulation results are given to illustrate the effectiveness of theoretical results. Key words: multi-agent systems; consensus; group consistency; interaction topology; system energy; optimal design 1 引引引言言言(Introduction) 当交互拓扑中有敌对交互或不连通时, 系统不一 多智能体系统的研究方兴未艾, 其一阶积分器系 定具备稳定性, 系统状态的一致性更难得到, 但可能