矩阵权重网络上多自主体系统的领航-跟随控制研究

目前多自主体系统协同控制的研究主要聚焦在网络连边权重为数值的数值权重网络上，但此类网络无法描述相邻自主体状态向量中不同维度分量之间的联系，造成对现实世界多自主体系统的建模失真。本项目以矩阵权重网络上多自主体系统为对象，克服网络结构和权重矩阵难以解耦分析带来的挑战，研究其领航-跟随控制方法。首先，基于矩阵值扰动Laplacian矩阵零空间分析，分别在同质和异质控制输入下，研究网络结构、权重矩阵、领航个体选择与系统实现协同跟踪和广义协同包围的关系，并结合积分图分析将结果推广到动态切换网络情形；随后，提出基于权重矩阵特征值的中心性指标，结合网络结构和权重矩阵的代数性质，研究领航个体选择与系统收敛速率的关系；最后，设计基于邻居选择机制的完全分布式算法，在保证控制输入到所有自主体可达性的基础上简化网络结构，优化系统收敛速率。本项目突破现有多自主体系统研究框架，具有重要的理论意义。

Current works on distributed cooperative control of multi-agent systems mainly concentrate on scalar-weighted networks, which ignore the interdependency amongst the elements in state vectors between neighboring agents and, therefore, cannot characterize the real-world multi-agent systems accurately. This project studies the leader-follower control of multi-agent system on matrix-weighted networks, where the challenges arise since analysis of network structure and weight matrices cannot be decoupled. First, based on the analysis of null space of matrix-valued perturbed Laplacian, the influence of network structure, weight matrices, and leader selection on the leader-follower tracking and containment control is to be studied for homogeneous and heterogeneous control input cases, separately, the results are to be extended to switching matrix-weighted networks via integral graph analysis; Then, based on the spectrum of weight matrices, novel centralities are to be proposed for analyzing the influence of leader selection along with the algebraic properties of the network structure and weight matrix on the convergence rate of the system. Finally, a fully distributed network reduction algorithm is to be designed based on the idea of neighbor selection, where network reachability can be guaranteed and the convergence rate can be optimized as well. This project breaks through the limitations of the existing multi-agent system interaction protocol framework and is expected to promote a breakthrough in the theory of multi-agent systems.