复杂网络可控性研究现状综述

Recent progress in controllability of complex network

控制复杂系统是人们对复杂系统模型结构及相关动力学进行研究的最终目标,反映人们对复杂系统的认识能力.近年来,通过控制理论和复杂性科学相结合,复杂网络可控性的研究引起了人们的广泛关注.在过去的几年内,来自国内外不同领域的研究人员从不同的角度对复杂网络可控性进行了深入的分析研究,取得了丰硕的成果.本文重点讨论了复杂网络的结构可控性研究进展,详细介绍了基于最大匹配方法的复杂网络结构可控性分析框架,综述了自2011年以来复杂网络可控性的相关研究成果,具体论述了不同类型的可控性、可控性与网络拓扑结构统计特征的关联、基于可控性的网络及节点度量、控制的鲁棒性和可控性的相关优化方法.最后,对网络可控性未来的研究动态进行了展望,有助于国内同行开展网络可控性的相关研究.

The model,structure and dynamics of complex systems and networks are studied to control complex systems,which reflects the ability to understanding complex systems.Recently,the research on controllability of complex networks by using control theory and complexity science has attracted much attention.It has been investigated extensively by many scientists from various fields,and many meaningful achievements have been obtained in the past few years.In this paper,the process of controllability of complex networks is discussed,the framework of structural controllability based on maximum matching is introduced in detail,and the relevant research status since 2011 is summarized.Controllabilities of complex networks are introduced in the following aspects：different types of controllabilities,relationship between controllability and network statistical characteristics,classification and measures based on controllability,robustness of controllability,and optimization methods of controllability.Finally,the questions urgent to solve in controllability are discussed,so as to give a help to the the study in this respect.There are five sections in this paper,which involve with different aspects of controllability.In the introduction section,the research work of controllability since 2011 is briefly mentioned,and the difference between controllability and previous pinning controllability is clarified.In the second section,the concept of controllability and different types of controllabilities are discussed in detail,including structural controllability,exact controllability,controllability with edge dynamics and controllability with nodal dynamics.In the third section,the relationship between controllability and network structure is investigated,especially the effects of common statistical characteristics and low-degree nodes on controllability.In the fourth section,the measures based on controllability are introduced,which includes control profiles,control range,control centrality,control capacity and control modality.In the fifth section,the research work about control robustness is discussed from robustness measures to optimization methods.In the fifth section,the optimization methods of controllability are introduced,which are classified into two different strategies：topology and edge direction.