非线性多智能体网络上的一致性

The multi-agent network, due to broad applications in many domains such as communication and control, is one of the frontier research fields in complexity science. Thereinto, consensus has been recognized as one of the core issues in multi-agent networks and a very important branch of collective dynamics fields...In this research project, we will consider some first-order, second-order and high-order models of nonlinear multi-agent networks with continuous (or discrete) dynamics. By using the theories of stability, graph and matrix, we can study their collective dynamics behaviors, such as identical consensus, cluster consensus, delay consensus and component consensus. First, we will construct some appropriate network topologies, establish a series of sufficient conditions to guarantee the asymptotic, component or practcal stability of the zero solution in the corresponding error systems, and accordingly give some novel control protocols on consensus. The protocols can fill a theoretical gap of consensus and enrich the theoretical results on nonlinear science. Next, we will discuss the internal mechanism of mutual influence on individual dynamics, topology and consensus on several networks with variable structure, and present some effective control strategies to facilitate the helpful consensus (or avoid the bad consensus). Finally, we will verify correctness and availability of the theoretical results by numerical simulations. Our results can provide some feasible principles to design and manage some multi-agent networks.

多智能体网络是复杂性科学研究的前沿，在通讯和控制等许多领域中均有广泛的应用。一致性是多智能体网络研究的核心问题之一，也是群体动力学领域中的一个重要分支。.本项目针对一些非线性多智能体网络的动力学模型(含一阶、二阶与高阶的连续型和离散型等)，运用稳定性理论、图论和矩阵理论，就恒同一致、滞后一致、聚类一致和部分分量一致等群体动力学行为展开探索。首先，通过构造合适的网络拓扑，获得相应误差系统保持零解渐近稳定、部分稳定或实用稳定的一系列充分条件，给出一些新颖的一致性控制协议, 弥补现有一致性理论的不足，丰富非线性科学的理论成果；然后，在几个动态网络上探讨个体动力学、拓扑结构和一致性相互影响的内在机制，提出一些有效的控制策略，以便在网络上促进有益（或抑制有害）的一致性发生；最后，用数值模拟验证理论结果的正确性和有效性。本项目的研究结果，可为有关人员设计和管理多智能体网络提供一些可行的准则。

多智能体网络是复杂性科学研究的前沿，在通讯和控制等许多领域中均有广泛的应用。一致性是多智能体网络研究的核心问题之一，也是群体动力学领域中的一个重要分支。. 本项目针对一些非线性多智能体网络的动力学模型(含一阶、二阶与高阶的连续型和离散型等)，运用稳定性理论、图论、脉冲控制理论和矩阵理论，就恒同一致、滞后一致、聚类一致、实用一致和部分分量一致等群体动力学行为展开探索。首先，通过构造合适的网络拓扑，获得相应误差系统保持零解渐近稳定、部分稳定或实用稳定的一系列充分条件，给出了一些新颖的一致性控制协议, 弥补了现有一致性理论的不足，丰富了非线性科学的理论成果；然后，在几个动态网络上探讨个体动力学、拓扑结构和一致性相互影响的内在机制，提出了一些有效的控制策略，以便在网络上促进有益（或抑制有害）的一致性发生；最后，用数值模拟验证理论结果的正确性和有效性。. 对本项目的研究，共发表相关学术论文26篇，其中被SCI收录17篇，被EI收录5篇。指导和培养青年教师3名，培养硕士13名。. 本项目的研究结果，可为有关人员设计和管理多智能体网络提供一些可行的准则。