异质多智能体系统的能控性研究

The heterogeneity of the multi-agent system refers to being different of agents’ dimension and dynamics, which has extensive application background and higher theoretical value in many fields such as physics, engineering and sociology, etc. This project will aim at the controllability of heterogeneous multi-agent systems. Based on intrinsic dynamics heterogeneity and networked heterogeneity, the corresponding controllability models and controllability algorithms will be constructed respectively. Furthermore, this project will investigate the relationship among the individual heterogeneity, network topology and the controllability based on agebraic graph theory and matrix theory. For different network topologies and communications restrictions, the project will study the complete controllability, partial controllability and group cntrollability of heterogeneous multi-agent systems, in which the agents are first-order integrator and second-order integrator, deduce the controllability conditions, as well as establish the controllability criteria. Using matroid theoretic approach, the project will design appropriate control inputs to realize the controllability of general linear heterogeneous multi-agent systems, and provide analysis to a unified theoretical framework for the controllability of heterogeneous multi-agent systems. Moreover, a simulation platform of heterogeneous multi-agent systems will be builded based on the proposed controllability algorithms. The controllability is the fundamental structural properties of multi-agent systems, which is the basis of further research on control and synthesis of multi-agent systems. The research of this project will help people better understand the operating mechanism of multi-agent systems, and enrich the way and methods of its control system, which has a strong theoretical basis and practical significance.

异质指智能体的维数、动态可能是不同的，这种特性使得多智能体系统在物理、工程和社会等领域具有广泛的应用背景和较高的理论价值。本项目研究异质多智能体系统的能控性问题。基于动力学异质和网络异质,建立异质多智能体系统能控性模型；利用图论和矩阵论系统深入研究个体异质性、网络拓扑结构与系统能控性之间的关系。针对不同网络拓扑结构和通信受限环境，研究由一阶和二阶积分器构成的异质多智能体系统的完全能控性、局部能控性、群能控性问题，推导出系统能控条件，建立系统能控判据。利用拟阵理论研究一般线性异质多智能体系统能控性，设计合理的控制输入，构建异质多智能体系统能控性的理论框架；进而设计异质多智能体系统控制仿真平台。能控性是多智能体系统的基本结构性质，是进一步开展多智能体系统控制与综合研究的基础。本项目的研究有助于人们更好的理解多智能体系统的运行机制，并能丰富其控制系统的方式和方法，具有很强的理论基础和现实意义。

异质指智能体的维数、动态可能是不同的，这种特性使得多智能体系统在物理、工程和社会等领域具有广泛的应用背景和较高的理论价值。对于多智能体系统的能控性，个体的异质特性往往会严重影响系统的协同性能，甚至导致系统不稳定。本项目中的异质特性主要体现在个体的自身动力学差异和网络差异。首先，针对在不同网络拓扑结构和通信受限环境下，研究了异质多智能体系统的完全能控性、局部能控性、群能控性问题，提出了多智能体系统的局部能控性与群能控定义，分别推导出系统完全能控、局部能控和群能控的图等价刻画条件；进一步建立了群能控的秩判据和PBH判据，并利用特征值和特征向量给出群与子群对于系统能控的影响。其次，建立了多时间尺度下的异质多智能体系统模型，设计出合理的控制输入，给出了多时间尺度下系统能控的充要/充分/必要条件，推导出多时间尺度下系统能控的代数判据；进一步分析了多时间尺度下连续多智能体系统的二阶群能控性。针对在不同网络拓扑结构和通信受限环境下多智能体系统的异步一致性与能控性问题，设计出合理的脉冲控制输入，研究了可测时变时滞的异步一致性问题。第三，研究了不同拓扑结构下异质多智能体系统的能观性，将该系统的邻接矩阵进行巧妙分解，并选择合适的输出向量，可以将异质多智能体系统的动力学建模为经典的LTI系统。基于切换理论，利用不变子空间性质，得到了异质多智能体系统能观性的一些代数特征。特别地，通过设计一个切换序列，得到了一个不能观子空间。进而，本项目系统深入地研究了多智能体系统能控性与个体内在动力学和网络拓扑之间的定性和定量关系。最后，基于能控性控制算法，构建了异质多智能体系统的能控性仿真平台。本项目的研究不仅有助于建立异质多智能体系统能控性的理论框架，而且在跟踪控制和跨域异构编队等工程领域具有重要的应用前景。通过本项目的实施，共发表20篇SCI期刊论文和3篇会议论文；培养8名硕士研究生。