网络化异质多智能体系统的协调动力学分析与控制

The networked multi-agent systems with nonidentical individual dynamics are more practical than that with identical individual dynamics. This project mainly studies the coordinated dynamics and control of networked nonidentical multi-agent systems from the viewpoint of dynamics and control. We will develop our research in the following three aspects: firstly, we will construct the model of networked nonidentical multiagent systems based on the real background. Particularly, we will establish some typical models of networked nonidentical multiagent systems. Secondly, we will design some simple, realistic and effective controllers based on the state feedback control, impulsive control, pinning control and other controls. Thirdly, we will analyze the coordinated dynamics of networked nonidentical multiagent systems such as consensus, quasi-consensus, cluster consensus and finite-time consensus; moreover, we will study the impact of the different controllers on the coordinated dynamics of networked nonidentical multiagent systems. The key research problem of this project is "Modeling, Coordinated Dynamics Analysis and Control Strategy Design of Networked Nonidentical Multiagent Systems". The results of this project are meaningful for the enrichment and improvement of the study of coordinated dynamics of networked nonidentical multiagent systems. Furthermore, our research results will have extensive applications for multiagent systems.

与具有相同动力学个体的多智能体系统相比，个体动力学相异的多智能体网络化系统更具有实际意义。本项目主要从动力学与控制科学的角度研究网络化异质多智能体系统的协调动力学及其控制，主要研究内容包括：首先，结合多智能体系统的实际背景，建立网络化异质多智能体系统的模型，着重建立几类典型的网络化异质多智能体系统的模型；其次，结合状态反馈控制、脉冲控制和牵制控制等方法，设计几类简单、实际且行之有效的控制算法；再次，分析网络化异质多智能体系统的一致性、拟一致性、聚类一致性和有限时间一致性等协调动力学，并且研究不同控制算法对网络化异质多智能体系统的协调动力学的影响。本项目的核心科学问题是"网络化异质多智能体系统的建模、协调动力学分析和协调控制算法设计"。本项目的成果将会丰富和发展多智能体系统的协调动力学研究，不仅具有重要的理论意义，同时还有广泛的应用价值。

本项目以异质复杂网络系统为研究对象，针对耦合机制、变时滞、可变号系数、不完全信息的一致性协议、牵制控制等，围绕时滞泛函微分系统周期解的存在性、网络化异质多振子耦合系统的同步及拟同步、高阶多智能体系统的一致性及拟一致性、网络化二阶异质多智能体系统的拟一致性等方面展开研究，主要研究内容包括：1）证明了一类具有时变系数矩阵的中立型算子的泛函微分系统周期解的存在性；2）研究了网络化同质Duffing型振子耦合系统的同步，给出了Duffing型振子耦合系统在有向图上的全局同步和无向图上的全局指数同步的充分性判据；3）证明了网络化异质Duffing型振子耦合系统在没有外部控制的情形下可以实现拟同步；当网络化异质耦合系统具有高度异质性时，通过设计牵制控制也可以实现拟同步。4）在不依赖于联合连通切换拓扑结构的情形下，证明了序列连通的异质复杂网络切换系统可以实现拟同步；5）提出了一个仅仅依靠部分自身绝对信息和部分与其邻居之间的相对信息的一致性协议，给出了高阶多智能体系统实现一致性或拟一致性的判定准则。本项目的研究丰富了异质复杂网络系统同步的研究结果，特别是为耦合机制下的网络化异质耦合系统的动力学分析提供了初步的探索方法和理论基础。