基于切换系统理论的多智能体系统在非连通切换拓扑下的协调控制

Cooperative control of multi-agent systems with switching topologies has become a hot research topic in field of system and control, which has theoretical importance and practical engineering applications. So far, most of the existing results are based on the assumption that all the sub-topologies are connected. However, the connectivity of topologies is always fragile in the practical applications, which brings new problems and challenges for the cooperation of multi-agent systems. In order to meet the urgent need and overcome the limitations, this research project aims at, from the switched system point of view, solving the cooperative control problems of multi-agent systems with partial disconnected switching sub-topologies or all disconnected switching sub-topologies by utilizing graph theory, matrix theory and switched system control theory. On this basis, the obtained theoretical results will be applied to the practical applications of distributed autonomous robotic systems, which can demonstrate the effectiveness of the theoretical results and the practical applications.

切换拓扑结构下的多智能体系统协调控制是当前控制领域的一个热点研究方向，具有重要的理论研究意义与广泛的实际工程背景。目前大部分研究成果以所有切换子拓扑结构具有连通性为前提，然而实际应用中拓扑结构的连通性往往是脆弱的，这为多智能体系统的协调控制带来了新的问题与挑战。本项目针对这一迫切需求以及已有结果的不足，将从切换系统的角度出发，综合利用图论、矩阵理论以及切换控制理论解决多智能体系统在具有部分非连通切换拓扑结构以及无连通切换拓扑结构下的协调控制问题。在此基础上，将得到的理论成果应用到分布式群体自主机器人系统，以验证理论结果的可行性和具体实现效果。

多智能体系统实现协调控制不仅依赖于单个智能体系统的动态特性还取决于多个系统间的通信网络拓扑结构。本项目从切换系统的角度针对实际应用中具有切换拓扑结构的多智能体系统，重点研究了具有部分非连通切换拓扑结构以及无连通切换拓扑结构的多智能体系统协同控制问题。基于多Lyapunov函数方法，给出了时间依赖切换拓扑下实现协同控制的充分性条件与协同控制器设计方法，讨论了切换拓扑对于协同控制性能的影响。在此基础上，进一步探索了所得到理论结果在实际多机器人系统中的应用，扩充和深化了切换系统理论的应用范围。