基于符号图理论的合作-竞争多个体系统的群体行为演化

项目名称： 基于符号图理论的合作-竞争多个体系统的群体行为演化

项目编号： No.61473061

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 胡江平

作者单位： 电子科技大学

项目金额： 80万元

中文摘要： 多个体系统群体行为涌现是复杂系统研究的一个重要问题。基于合作机制的多个体系统的协调群体行为研究已经取得了丰富的研究成果。然而，合作与竞争是复杂系统内单元之间最普遍的作用关系，复杂系统在合作、竞争共同作用下的群体行为涌现机制研究更具有普适性、挑战性。本项目为了研究合作-竞争多个体系统的群体状态演化与耦合网络之间的关系，将采用符号图理论、动力系统理论、现代控制理论、随机过程等理论和方法围绕以下三个内容来开展工作：1）研究同步、极化、群同步等群体行为与合作-竞争耦合网络结构平衡性之间的定量关系；2）针对个体状态演化动力学的不确定性提供一套基于自适应估计的极化策略，并应用于包围控制问题；3）针对耦合网络的不确定性建立动态随机符号耦合网络上的群体状态演化模型，分析其同步、极化、群同步的几乎处处收敛性，给出基于网络结构平衡性的相变临界条件。

中文关键词： 多个体系统；符号图理论；群体行为；结构平衡性；不确定性

英文摘要： The emergence of the collective behaviors of multi-agent systems is an important issue in the field of complex systems. Extensive results have been obtained for the coordinated collective behaviors of cooperative multi-agent systems. However, cooperation and competition are two elementary relationships between units in complex systems. It is more universal and more challenging to study the emergence mechanism of the collective behaviors under the joint action of cooperation and competition for complex systems. In order to investigate the relationship between the evolution of the collective state and the coupling network of a cooperation-competition multi-agent system, the project will use some appropriate theories and methods, including signed graph theory, dynamical systems theory, modern control theory, stochastic process, and so on, to deal with the following three issues: 1) The quantitative relation between the collective behaviors (i.e., synchronization, polarization and clustering) and the structural balance of the cooperation-competition coupling network has to be studied; 2) An adaptive estimation based polarization strategy has to be proposed for agent dynamics with uncertainties and then is applied to solve the containment control problem; 3) The evolution model of the collective state has to be built on a dynamic signed network with random uncertainties. The almost sure convergence of synchronization, polarization and clustering has to be analyzed. The phase transition condition, which depends on the structure balance of the coupling network, has to be provided explicitly.

英文关键词： Multi-agent systems;Signed graph theory;Collective behavior;Structural balance;Uncertainties