基于平均理论的高阶线性多智能体系统趋同控制问题研究

Recently, consensus of high-order linear multi-agent systems has received much attention by many researchers. Current focus on this problem mainly puts emphasis on dealing with fixed network topology, with relatively few attention on the case of switching one. The averaging theory, which was initially proposed in celestial mechanics and was further developed in systems science, is a fundamental tool to investigate the stability of time-varying systems. Currently, the application of averaging theory to the field of consensus control of multi-agent systems under switching topology has just started, and there are many important issues to be solved. In this project, we provide some averaging-based consensus control algorithms for high-order liner multi-agent systems under switching topology. The following issues will be addressed. (1)The consensus controllability and observability of linear multi-agent systems under switching topoloty are examined, generalizing existing results which are limit to fixed topology. Furthemore, the dual principle betwee consensus controllability and consensus observability is explored. (2)Based on the consensus controllability and observability, the consensus control algorithms, which characterize the state couplings or output couplings among agents, are proposed by the tool of averaging method. Our algorithms generalize the existing results which are only valid for multi-agent systems whose node dynamics is neutrally stable. (3)The separation theory of the distributed observers for multi-agent systems is developed, which is used to the observer-based consensus control.

近年来，高阶线性多智能体系统的趋同控制引起了国内外学者极大的关注。目前这方面的研究主要集中在固定拓扑下的趋同控制，切换拓扑下的结论相对较少。平均理论作为天体力学和系统科学中研究时变系统稳定性的常用工具，最近被应用到切换拓扑下的多智能体系统趋同控制理论中。这方面的工作刚刚起步，有许多理论和应用方面的难题亟需解决。本项目应用平均理论研究切换拓扑下的高阶线性多智能体系统的趋同控制问题，具体包括：(1)研究切换拓扑下的线性多智能体系统的趋同能控性和趋同能观性，推广现有文献中固定拓扑下的趋同能控性和趋同能观性工作。讨论趋同能控性和趋同能观性之间的对偶原则。(2)在趋同能控性和趋同能观性的基础上，研究状态耦合型和输出耦合型趋同算法，放宽了现有文献中对节点线性系统中性稳定的假设，而只要求其能控能观。(3)发展基于分布式观测器的趋同控制理论，研究分布式观测器理论之分离性原理。

多智能体系统由分布式人工智能演化而来，重点研究分布式系统交互行为的基本定理和结构关系，是国际上的研究热点。多智能体系统趋同问题的根本任务是研究个体局部的低等行为怎样构建复杂且和谐的群集行为。个体间的交互方式，即网络拓扑，是系统集体行为形成的一个关键。切换拓扑下的趋同控制是该领域的难点之一。针对该问题，我们对高阶线性多智能体系统进行了深入的研究，提出了基于平均理论的趋同分析和算法框架。本项目针对已有研究成果中的局限，交叉融合平均理论、快周期时变理论、快切换系统理论等多种方法和技术，结合代数图论及多尺度分析，发展了切换拓扑下的线性多智能体系统的趋同分析和相应的算法设计，取得的研究成果主要包括以下四个方面：（1）给出了切换拓扑下趋同能控性/趋同能观性的定义和判据；（2）给出了状态耦合型趋同方案和基于观测器状态耦合的趋同方案，揭示了分布式对偶原理和分布式分离性原理；（3）将基于确定性平均理论的趋同方案初步推广到随机情形，找到了基于随机平均理论趋同方案的突破口；（4）给出了基于平均理论的趋同问题的若干应用，包括分布式优化问题，分布式事件驱动控制及分布式输出调节问题等。..项目成果主要以学术论文形式体现，已发表标注本项目资助的论文29篇，其中，SCI检索期刊论文25篇，EI期刊论文3篇，会议论文1篇，指导与本项目相关的硕士研究生3名。