随机通信受限下网络同步与一致问题研究

Synchronization of complex networks and consensus of multi-agent systems is a hot research topic in the field of complex systems in recent years. This project is aimed to study the problem of synchronization of complex networks and consensus of multi-agent systems by utilizing the methods of stochastic process, control theory, graph theory and matrix analysis. First, in order to establish the model of networks and multi-agent systems under random communication constraints, we will employ Bernoulli variables with constant expectation, Bernoulli variables with time-varying expectation and Markov chain to characterize different random communication constraints, such as randomly occurring communication delay, randomly occurring self-feedback delay, randomly occurring sensor saturation, state-dependent noise and random packet dropout. Second, the problem of synchronization of complex networks and consensus of multi-agent systems under one or multiple randomly occurring events will be investigated by using control theory, stochastic differential equation, graph theory and Razumikhin method. By this way, the impacts of randomly occurring events on the performance of synchronization and consensus will be revealed. Finally, based on the above results, we further utilize evolutionary computation methods to investigate the pinning control problem of networks under random communication constraints. The obtained results will be applied to the field of synchronization of neuronal networks. This project will not only be beneficial to better understanding the intrinsic mechanisms of synchronization and consensus in real-life complex systems, but also will provide theoretical methods and instructions for the synchronization of complex networks and coordination of multi-agent systems.

网络同步和多智能体系统一致是近年来复杂系统领域里的一个热点问题。本项目旨在用随机过程、控制理论、图论以及矩阵分析等方法研究复杂动态网络的同步和多智能体系统的一致问题。首先，通过使用期望不变的贝努利随机变量、期望时变的贝努利随机变量和马尔科夫链等描述网络中普遍存在的随机各种通信限制 (通信时滞、自反馈时滞、传感器饱和、状态依赖噪声、丢包等)，建立随机通信受限下的网络和多智能系统模型; 其次，应用控制理论、随机微分方程、图论、Razumikhin方法研究一种或多种随机发生事件下的网络同步和一致问题，刻画随机发生事件对于网络同步和一致的影响; 在前两者研究基础之上，采用进化计算方法研究随机通信受限下的网络牵制问题，同时以期将结果应用到神经元网络同步。本项目研究将有助于更好地理解现实复杂系统中同步和控制的内在机理，为复杂网络同步、多智能体的协同控制设计提供理论依据和方法上的指导。

网络环境下的同步和一致问题是一个数学、统计、控制和计算方法等领域的一个交叉学科。本项目旨在用随机过程、控制理论、图论以及矩阵分析等方法研究复杂动态网络的同步和多智能体系统的一致问题。首先，通过使用期望不变的贝努利随机变量和马尔科夫链等描述网络中普遍存在的随机各种通信限制 (通信时滞、自反馈时滞、状态依赖噪声、丢包等)，建立随机通信受限下的网络和多智能系统模型; 其次，应用控制理论、随机微分方程、图论等方法研究一种或多种随机发生事件下的网络同步和一致问题，刻画随机发生事件对于网络同步和一致的影响; 在前两者研究基础之上，采用进化计算方法研究随机通信受限下的网络牵制问题，同时将结果应用到神经元网络同步的理论研究中。..本项目的研究成果在Nature子刊、IEEE汇刊、IFAC汇刊、美国物理学会会刊发表论文近20篇(包括10余篇IEEE汇刊长文)，较好的完成了预期目标。项目的执行，从一定意义上促使人们对于网络化环境下的复杂网络同步以及一致问题有更深入的理解。