基于符号图理论的多个体系统分组蜂拥控制研究

Recently, flocking control problems in multi-agent systems have received extensive attention. The researchers have proposed many models for flocking which are all based on cooperative systems, i.e., the cooperative relationship among the agents generates the entire flocking behavior. However, the relationship between agents is sometimes very complex and there exist not only cooperative relationship, but also competitive relationship. Because of the existence of competitive relationship, the systems cannot take on the entire flocking behavior, but instead take on cluster flocking behavior. To solve the cluster flocking control problem for the case of the existence of competitive relationship among the agents, this project studies the cluster flocking control problem of multi-agent systems. Based on the signed graph theory, we first investigate the cluster flocking control problem of multi-agent systems with linear velocity couplings, then investigate the cluster flocking control problem of multi-agent systems with nonlinear velocity couplings to obtain the robustness and finite convergence of cluster flocking behavior and finally investigate the cluster flocking control problem of multi-agent systems with collision avoidance to avoid collisions among the agents. This project will not only enrich and perfect the theories related to flocking control problems but will also provide theoretical basis for the application of flocking control problems.

近年来，多个体系统蜂拥控制问题的研究受到了广泛关注。研究者们提出了许多基于合作系统的蜂拥数学模型，即个体间通过合作关系产生整体蜂拥行为。然而，个体间的关系往往是十分复杂的，不但有合作关系，还常常伴有竞争关系。由于竞争关系的存在，系统不可能呈现整体蜂拥行为，而是会呈现出分组蜂拥行为。为解决个体间存在竞争关系时系统的分组蜂拥控制问题，本课题研究多个体系统的分组蜂拥控制问题。基于符号图理论，首先我们研究线性速度耦合的多个体系统分组蜂拥控制问题；其次，为了得到分组蜂拥行为的鲁棒性和有限时间收敛，我们研究非线性速度耦合的多个体系统分组蜂拥控制问题；最后，为了避免分组过程中个体间发生碰撞，我们研究带有碰撞避免的多个体系统分组蜂拥控制问题。本课题不仅丰富和完善蜂拥控制问题相关理论，还将为该问题在工程上的应用提供理论依据。

近年来，多个体系统蜂拥行为吸引了来自数学、物理、控制、生物等众多研究领域研究者们的关注。人们从各自的研究领域对这类多学科交叉的热点问题进行研究。本项目致力于解决竞争关系下多个体系统的蜂拥行为问题。针对复权图—比符号图更一般的图，我们系统研究了它的代数性质以及复权图上多个体系统的相关分组蜂拥问题。通过对相应蜂拥模型的建立与分析，得到了蜂拥行为发生的条件。通过本项目的研究，项目负责人正式发表（或录用等待发表）学术论文9篇， 其中国际SCI期刊论文7篇，有4篇论文发表在国际应用数学、控制理论顶级期刊Mathematical Models and Methods in Applied Sciences，IEEE Transactions on Automatic Control和Automatica上。