有向相依网络的可控性研究

针对相依方式对有向相依网络可控性的影响,研究了不同相依方式下有向相依网络的可控性。通过构建基本的有向相依网络模型,结合严格可控性理论,给出了可控性评判指标。同时基于经典的有向随机网络和有向无标度网络,提出3种有向相依网络模型,并研究了随机相依条件下有向相依网络的可控性。随后定义了3种相依方式,并对比分析了在不同相依方式下有向相依网络的可控性。结果表明,在同等相依比例下,基于最低入度与最低出度节点相依的有向相依网络可控性最强,而基于最高入度与最高出度节点相依的有向相依网络可控性最弱,研究成果能够为实际有向相依网络的构建提供有益的参考和指导。     

割点失效对复杂网络可控性的影响

信息物理系统个体间的相互作用能够应用复杂网络描述,复杂网络中的某些节点遭到攻击或破坏会造成网络故障,导致整个网络系统不受控.割点是网络中的一类关键节点,受攻击或故障后将导致网络连接断开,在保证网络连通性方面发挥着重要作用,但割点失效对网络可控性的影响尚不清楚.鉴于此,给出复杂网络中割点失效的可控性模型,研究割点失效对可控性的影响,同时选取节点的随机失效和以度为依据的蓄意攻击作为对比.研究发现:随机失效对可控性的影响较小,割点失效和蓄意攻击对可控性的影响较大;平均度较低时割点失效和蓄意攻击对可控性影响基本相同,但平均度增大后,割点失效比蓄意攻击对可控性的影响更大;另外,平均度的增加能够提高网络对割点失效的控制鲁棒性.     

Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network's Structural Controllability

Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level, in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications, we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity, we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure.      

Pinning control and controllability of complex dynamical networks

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.     

城市供水系统故障蔓延动力学研究

基于复杂网络理论,建立了城市供水系统故障蔓延动力学模型,模型考虑了城市供水复杂网络结点的自修复功能、故障蔓延机制。研究了自修复因子、延迟时间因子两个特征参数对三种应用广泛的城市供水复杂网络（随机网络、无尺度网络和小世界网络）结点修复率和故障结点数的影响。模拟结果与实际城市供水系统的特征一致,表明所建立的模型可以有效地模拟城市供水系统故障蔓延动力学。     

大系统控制论与复杂网络——探索与思考

随着通信技术和网络技术的飞速发展, 在社会、经济乃至日常生活领域中, 出现了越来越多的复杂动态网络. 网络科学作为一门新兴的交叉学科, 对复杂动态网络性能特征、演化进程和控制方法的研究已取得了丰富的成果. 大系统控制论以高维动态大系统的行为分析和控制优化为主要研究内容, 应该能为复杂网络的研究提供有益的借鉴. 本文针对复杂动态网络研究的一些热点问题, 探索了用大系统控制理论和方法解决复杂网络结构分析和控制的可能性, 分析了面临的困难和应对的思路. 针对大规模复杂动态网络的控制和优化, 提出了集网络科学的宏观分析方法、控制科学的定量设计方法和信息科学的智能处理方法于一体的多层递阶结构.     

Input addition and leader selection for the controllability of graph-based systems

In this paper, we consider dynamical graph-based models, which are well fitted for the structural analysis of complex systems. A significant amount of work has been devoted to the controllability of such graph based models, e.g. recently for multi-agent systems or complex networks. We study here the controllability through input addition in this framework. We present several variants of this problem depending on the freedom which is left to the designer on the additional inputs. We use a unified framework, which allows us to encompass the different applications and representations (large scale systems, complex communications networks, multi-agent systems, …) and provide convenient graph tools for their analysis. Our contribution is to characterize the structural modifications of the system resulting from an input addition (or a leader selection) and of the mechanisms which lead to controllability. We provide information on the possible location of additional inputs and on the minimal number of inputs to be added for controllability.     

节点分类及失效对网络能控性的影响

复杂系统间的相互作用能够用复杂网络描述.复杂网络中某些节点遭受攻击或破坏会造成网络故障,导致整个网络能控性变化.不同节点失效会对网络能控性有不同的影响.本文提出一种网络节点的分类方式,将网络中的节点根据边的方向和匹配关系分成九种类型,并给出了辨识节点类型的算法.另外,本文给出了基于此分类方式下复杂网络中某类节点失效时,...     

Controllability emerging from conditional path reachability in complex networks

Controllability of complex networks is a fundamental requirement to orientate the networks toward a sustainable way of development. Determination of link weights and calculation of eigenvalues of large‐scale matrices are two inevitable problems in applying the exact controllability framework in complex networks. Here, we introduce a novel controllability analysis approach based on the controllability index and the reachability matrix to identify the minimum set of driver nodes, in order to achieve complete regulation of arbitrary networks with general configurations. An effective algorithm is theoretically developed via using only the 0–1 binary structure of the network. Theoretical analysis and numerical examples show that our proposed algorithm possesses structural adaptability and control robustness under the weighted perturbation. Copyright © 2017 John Wiley & Sons, Ltd.     

CPS拓扑结构节点重要性排序方法

信息物理融合系统(Cyber-physical Systems,CPS)拓扑结构中节点重要性排序是CPS拓扑分析的重要方面。针对CPS内在结构特征,构建一种CPS拓扑结构模型——交互网络模型。然后结合CPS信息交互特点定义节点交互介数作为衡量具体节点重要性度量,阐明该测度能够反映节点的相对重要度,并给出了时间复杂度为多项式阶的节点重要性排序有效算法。最后构建CPS拓扑实例进行分析,并与节点介数进行对比,说明节点重要性排序能够为CPS的运行和防护提供重要参考。     

Spatiotemporal Input Control: Leveraging Temporal Variation in Network Dynamics

The number of available control sources is a limiting factor to many network control tasks. A lack of input sources can result in compromised controllability and/or sub-optimal network performance, as noted in engineering applications such as the smart grids. The mechanism can be explained by a linear time-invariant model, where structural controllability sets a lower bound on the number of required sources. Inspired by the ubiquity of time-varying topologies in the real world, we propose the strategy of spatiotemporal input control to overcome the source-related limit by exploiting temporal variation of the network topology. We theoretically prove that under this regime, the required number of sources can always be reduced to 2. It is further shown that the cost of control depends on two hyperparameters, the numbers of sources and intervals, in a trade-off fashion. As a demonstration, we achieve controllability over a complex network resembling the nervous system of Caenorhabditis elegans using as few as 6% of the sources predicted by a static control model. This example underlines the potential of utilizing topological variation in complex network control problems.      

复杂网络能控性鲁棒性研究进展

研究复杂网络能控性鲁棒性对包括社会网络、生物和技术网络等在内的复杂系统的控制和应用具有重要价值. 复杂网络的能控性是指: 可通过若干控制节点和适当的输入, 在有限时间内将系统状态驱动至任意目标状态. 能控性鲁棒性则是指在受到攻击的情况下, 复杂网络依然维持能控性的能力. 设计具有优异能控性鲁棒性的复杂网络模型和优化实际网络的能控性鲁棒性一直是复杂网络领域的重要研究内容. 本文首先比较了常用的能控性鲁棒性定义及度量, 接着从攻击策略的角度分析了3类攻击的特点及效果, 包括随机攻击、基于特征的蓄意攻击和启发式攻击. 然后比较了常见模型网络的能控性鲁棒性. 介绍了常用优化策略, 包括模型设计和重新连边等. 目前的研究在攻击策略和拓扑结构优化方面都取得了进展, 也为进一步理论分析提供条件. 最后总结全文并提出潜在研究方向.     

Modelling uncertainty in social–natural interactions

Socio-ecological systems can be represented as a complex network of causal interactions. Modelling such systems requires methodologies that are able to take uncertainty into account. Due to their probabilistic nature, Bayesian networks are a powerful tool for representing complex systems where interactions between variables are subject to uncertainty. In this paper, we study the interactions between social and natural subsystems (land use and water flow components) using hybrid Bayesian networks based on the Mixture of Truncated Exponentials model. This study aims to provide a new methodology to model systemic change in a socio-ecological context. Two endogenous changes – agricultural intensification and the maintenance of traditional cropland – are proposed. Intensification of the agricultural practices leads to a rise in the rate of immigration to the area, as well as to greater water losses through evaporation. By contrast, maintenance of traditional cropland hardly changes the social structure, while increasing evapotranspiration rates and improving the control over runoff water. These results indicate that hybrid Bayesian networks are an excellent tool for modelling social–natural interactions.     

一种具有核心-边缘结构的无标度网络演化模型

核心-边缘结构是复杂网络中一种重要且常见的簇团结构,相关研究一直较少。为了研究复杂网络核心-边缘结构的相关特性,分析了随机块模型的结构,并在此基础上提出了一种具有无标度特性的核心-边缘结构网络演化模型。通过理论和数值分析,验证了所生成的网络具有较好的无标度特性和核心-边缘结构,且其结构的紧密程度可调,为进一步研究复杂网络核心-边缘结构的相关特性提供了基础。     

复杂动态网络环境下控制理论遇到的问题与挑战

以漫谈的方式讨论复杂动态网络环境下传统控制理论所遇到的一些新问题与新挑战. 具体地, 本文首先介绍现代网络科学与工程的背景, 然后讨论复杂动态网络的牵制控制、有向复杂网络的能控性以及"网络的网络"的 建模与控制等三个方面的相关科学研究问题.     

多智能体系统能控性研究进展

能控性问题是多智能体协调控制领域中一个基本又十分重要的研究课题.本文对多智能体系统能控性问题的研究现状进行综述.介绍了多智能体能控性领域的基本问题和特点,并结合智能体自身动力学与邻居交互协议,从拓扑结构角度对该领域当前的研究热点和前沿进行分析阐述.进一步,对结构能控性的研究成果进行归纳总结,并对能观测性、可镇定性和复杂网络能控性等相关问题进行阐述.最后给出了仍需解决的问题和可能的研究方向.     

注意力流网络中节点影响力的层级性研究

复杂网络中节点影响力的层级性在网络结构与控制研究中至关重要。针对有向加权网络中节点影响力的层级性问题,基于海量在线用户行为数据,构建有向加权集体注意力流网络。通过定义节点的层级位置时间和位置约束指标,并结合节点的拓扑位置和时间序列,提出一种用于有向加权网络的节点影响力度量及排序算法。实验结果表明,该算法能有效区分网络层级结构,准确识别出最具影响力的节点,对于节点影响力评估与复杂网络可控性研究具有一定的借鉴意义和参考价值。     

一种基于RBF网络提取模糊规则的算法实现

径向基函数网络和模糊推理系统在一些柔和的情况下具有等价的功能,因此可以利用神经网络的学习算法来调节模糊系统的参数,学习后的模糊系统具有自学习和自组织性,但是削弱了模糊系统的可解释性。将模糊逻辑推理与神经网络控制技术相结合,分析了一种改进的径向基函数(RBF)神经网络结构,这种模糊神经网络结构能够有效地表达模糊系统可解释性这一突出特点,也使模糊系统具有了较好的自学习和自组织能力、通过VC 实现了基于这种RBF网络结构提取模糊规则的算法,并进行了仿真实验,仿真结果表明该算法是比较有效的。     

基于结构熵的注意力流网络异构性研究

结构熵作为复杂网络无序程度度量的重要手段,反映了网络内结构的异质性。传统结构熵在刻画复杂网络异构性时只关注网络结构中的“点”和“边”,表征注意力流网络结构的异构性特征时存在不足。对此,基于在线点击行为数据构建注意力流网络,在传统网络结构熵的基础上,综合考虑站点的边权重、站点的总停留时长等网络特征属性,定义了结构熵模型。进而,从站点的流强度、吸引注意力的能力等指标计算站点综合力,提出了注意力流网络异构性度量算法ANSE。实验结果表明,提出的结构熵可以有效地反映注意力流网络的结构特征,准确地度量注意力流网络中站点之间的差异性,分析站点重要性排序,通过和传统经典算法对比,在站点影响力排名上证明了该算法的优越性和有效性。     

EEG信号构建的复杂网络同步稳定性分析

人脑是自然界最复杂的系统之一,脑网络作为复杂网络理论在神经科学中的重要应用,为脑疾病的病理机制提供了新的研究方向。同步性作为影响网络性能的指标,对于复杂网络有着重要影响。为了研究同步性在脑网络中的表现,利用EEG动力学方程对120例酗酒病人的EEG信号进行复杂网络模型构造,根据所构造的模型利用李雅普诺夫稳定性理论进行证明。并通过实验对正常人和酗酒者脑网络同步状态做出统计,给出了酗酒病人和正常人的脑网络同步差异,可以揭示酗酒疾病对于人脑在功能结构上的影响,对其他疾病提供研究思路。