【作者】 周洁；

【导师】 聂森；

【作者基本信息】 华东交通大学 ， 控制科学与工程， 2022， 硕士

【摘要】 复杂网络控制问题是近几年网络科学研究领域中的一个热门话题,同时也是复杂网络研究的重要目标。网络的可控性能是系统控制研究中的一个基础问题,当系统在有限时间内通过有限外界输入能够实现从任意初态到任意终态的转移,那么这个系统就是可控的。在网络的可控性能研究中,基于结构可控性能的计算方法给出了有向网络实现完全控制所需要的最少外界输入数目,而基于严格可控性能的计算则进一步解决了无向及任意网络中最小驱动节点集的求解问题。随着网络控制问题的深入研究,人们发现即使网络在满足可控性能计算方法所确定的外界输入下驱动,依然难以实现运行状态的任意转移,其运行状态受到控制时间和控制能量等因素制约。因此网络控制问题的研究逐渐聚焦于关注网络的实际控制性能,如网络实现完全可控所需的能量消耗。复杂网络的控制性能与网络的拓扑结构特性紧密相关,网络结构的特征会影响系统实现控制所需的能量消耗。割点作为网络结构中的一类关键节点,其在网络的连通性中起到关键作用。割点的删除会使得网络的连通性能发生改变,进而对系统其他性能产生影响。现有的研究分析了割点失效对于系统可控性能及抗毁性能的影响,但割点在网络控制中所起到的作用以及其对网络控制特性的影响仍缺乏相关的研究。本文基于割点的结构特性,探讨了其在网络控制中的作用。首先分析了割点和网络中最少驱动节点之间的关联。结果表明最小驱动节点集中的节点选取会避开割点。而从网络控制能量优化的角度考虑,选择割点作为驱动节点,能够明显降低网络可控所需要的能量,这与割点在网络控制路径中所处的位置相关。另外,本文通过对比不同类型的节点失效策略,分析了节点失效对网络控制能量的影响。结果表明,相较于随机节点失效,割点的失效会显著增大网络控制所需的能量消耗,即割点在网络的控制能量优化中具有重要的作用。更多还原

【Abstract】 The research on the control characteristics of complex networks is a hot topic in the researching direction of complex networks in recent years,and the problem of network controllability is also an important goal of complex network research.With the in-depth study of complex networks,people have found that when a network selects appropriate driving nodes so that the network can reach the desired target state,then the network is controllable.In the controllability of complex networks,structure controllability studies the minimum input required when the network is completely controllable,while exact controllability further solves the controllability problem in networks with different structures.However,research in the control of complex networks shows that even though some networks meet the controllability requirements of the network in theory,the cost or time required in the control process is too high,which is not in line with the actual requirements.In view of this phenomenon,the control energy problem of complex network is studied,and the control energy of network can be reduced by adopting a reasonable control method.For the complex networks,the control performance of complex networks is affected by the characteristics of their network structures.As a type of key nodes in the network structure,cut vertexes are essential for network connectivity because their removal will disconnect the network.Despite their fundamental importance,the influence of cut vertexes on network control is still uncertain.Therefore,by studying the cut vertexes,we can find out what effects the cut vertexes have on the network control performance.Here,we reveal the relationship between cut vertexes and driver nodes,and find that driver nodes tend to avoid cut vertexes.In the control energy of the network,driving cut vertexes reduces the energy required for controlling complex networks,since the cut vertexes are located near the middle of the longest control chains.By employing three different node failure strategies,we investigate the impact of cut vertexes failure on the energy required.The results show that cut vertex failures markedly increases the control energy because cut vertexes are larger-degree nodes.Our results deepen the understanding of the structural characteristic in network control.更多还原