多智能体系统的能控性与可镇定性研究

Controllability and stabilizability of multi-agent systems are hot issues in the study of complex intelligent systems in recent years. Most of the existing research results mainly focus on the homogeneous multi-agent systems and generally assumes that the network communication is unconstrained. In this project, the controllability with communication constraints and edge dynamics, and the stabilizability of heterogeneous multi-agent systems will be considered. First of all, through analyzing the effect of communication constraints on controllability, some conditions for robust controllability and controllability preservation of multi-agent systems will be established. By optimizing the communication topologies and assigning the link weights, the controllability of multi-agent systems with communication constraints will be realized. Secondly, the edge controllability model will be constructed and the definition of edge controllability will be proposed. Some criteria for edge controllability will be established. In addition, the manipulative edge selection and the weight assignment algorithms with polynomial time complexity will be presented. Finally, through analyzing the relationship among the individual heterogeneous, network topology and stabilizability, some necessary and sufficient conditions for solving the stabilizability problem of heterogeneous multi-agent systems will be obtained. Moreover, the appropriate control protocols will be builded based on the proposed theoretical results of stabilizability to complete the formation control and tracking control of heterogeneous multi-agent system. The project will help us to enrich and perfect the theoretical framework of distributed coordination of multi-agent systems, and provide the theory supporting for the practical application of multi-agent systems.

多智能体系统的能控性与可镇定性是近年来复杂智能系统研究中的热点问题。现有的研究主要针对具有相同节点动力学的多智能体系统，且一般假设网络通信是无约束的。本项目研究具有通信约束和边动力学的能控性和具有自身动力学异质的可镇定性。首先，分析通信约束对能控性的影响，建立多智能体系统鲁棒能控性和能控性保持的条件，优化拓扑结构、选择合理的连接边权重值以实现通信约束条件下多智能体系统的能控性。其次，构建边能控性的模型，提出边能控性的定义，建立多智能体系统边能控性的判据，设计具有多项式时间复杂度的控制边选取和边权配置算法。最后，分析动力学异质、拓扑结构和可镇定性的关系，获得异质多智能体系统可镇定性的充要条件。进一步，应用可镇定性的理论结果，设计适当的控制协议以实现异质多智能系统的跟踪和编队控制。本项目的研究不仅有助于丰富和完善多智能体系统的协调控制理论，同时也能为多智能体系统的实践应用提供理论支持。

多智能体系统的能控性与可镇定性是近年来复杂智能系统研究中的热点问题。现有的研究主要针对具有固定无向拓扑的多智能体系统，且一般假设网络通信是无约束的。本项目采用图论、矩阵理论、稳定性理论、控制理论等工具研究了具有不同网络拓扑结构和通信约束的多智能体系统能控性和的可镇定性。首先，分析了有向拓扑下的能控性，建立了能控性的代数和图论判据，优化拓扑结构、选择合理的连接边权重值实现了通信约束条件下多智能体系统的能控性。其次，构建了通信约束下的能控性的模型，建立了具有切换拓扑、采样数据和切换动力学的多智能体系统的能控性判据，设计了具有多项式时间复杂度的控制节点选取和边权配置算法。最后，分析了离散时间动力学、拓扑结构和可镇定性的关系，获得了离散线性多智能体系统可镇定性的充要条件。进一步，应用可镇定性的理论结果，设计适当的控制议，实现了多智能系统的跟踪和编队控制。以上成果已发国际SCI期刊论文14篇，尚有部分成果在整理中。参与本项目的六名研究生已毕业，其中两名研究生获得博士学位。本项目的研究不仅丰富和完善了多智能体系统的协调控制理论，同时也为多智能体系统的实践应用提供了理论支持。