Comparison between pinning control of different chaotic complex dynamical networks

The stabilization properties of various typical complex dynamical networks composed of chaotic nodes are theoretically investigated and numerically simulated in detail. Some local stability properties of such pinned networks are derived and the valid stability regions are estimated based on eigenvalue analysis. Numerical simulations of such networks are given to explain why significantly less local controllers are needed by the specifically pinning scheme, which pins the most highly connected nodes in scale-free networks, than that required by the randomly pinning scheme. Also, it is explained why there is no significant difference between the two schemes for controlling random-graph networks and small-world networks.

Disturbance rejection and H_∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabasi-Albert model and various star-shaped networks are performed for verification and illustration.

Controllability robustness of complex networks

This article presents an overview on the state-of-the-art development in complex network controllability and its robustness against malicious attacks and random failures.Specifically,it first reviews the concepts of network pinning control and controllability,and then discusses the network controllability robustness against destructive attacks by means of node-and/or edge-removal.The related issue of network connectivity robustness is also discussed.To that end,it furthermore provides an brief overview on the recent development of a machine-learning approach for predicting optimal network controllability robustness,which may shed some lights on the understanding of optimal network structures for various design considerations.

Pinning control of complex Lur’e networks

This paper addresses the control problem of a class of complex dynamical networks with each node being a Lur＇e system whose nonlinearity satisfies a sector condition, by applying local feedback injections to a small fraction of the nodes. The pinning control problem is reformulated in the framework of the absolute stability theory. It is shown that the global stability of the controlled network can be reduced to the test of a set of linear matrix inequalities, which in turn guarantee the absolute stability of the corresponding Lur＇e systems whose dimensions are the same as that of a single node. A circle-type criterion in the frequency domain is further presented for checking the stability of the controlled network graphically. Finally, a network of Chua＇s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.

Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network

This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays. Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations, as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks. It is shown that, through Lyapunov stability theory, distributed adaptive controllers con- structed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks, and perturbation inputs. A Chua＇s circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.

A survey on complex dynamical networks with impulsive effects

We review the research on complex dynamical networks(CDNs)with impulsive effects.We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects,where impulsive effects are considered from two aspects,i.e.,impulsive control and impulsive perturbation.Five aspects of CDNs with impulsive effects are surveyed,including synchronizing impulses,desynchronizing impulses,adaptive-impulsive synchronization,pinning impulsive synchronization,and CDNs with stochastic and impulsive effects.Finally,conclusions and some future research directions are briefly addressed.

Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.

带有通信噪声的随机时延复杂动态网络的H_∞控制

考虑到复杂动态网络节点之间信息传输不可避免地受到信道噪声干扰以及传输时延的随机发生,提出了一种新的控制策略,使复杂动态网络在均方意义下渐近稳定,且满足一定的H∞性能指标.将复杂动态网络的节点信息在传输过程中存在的时延描述成Markov链形式,利用Lyapunov稳定性理论、随机分析理论与H∞控制方法,建立了随机时延复杂动态网络控制器存在准则.最后,以Lorenz混沌系统作为节点动力学,构造复杂动态网络,并且用数值仿真的方法验证了所提出的控制器能够将具有随机时延且受到通信噪声扰动的复杂动态网络渐近稳定在平衡点,满足一定H∞性能指标要求.

一种网络化控制系统的鲁棒H_∞动态输出反馈控制

对于存在网络诱导控制时延和输出时延的网络化控制系统,在离散域内给出了网络化控制系统的一种时延相关的动态输出反馈控制方法.针对无扰动和有扰动的系统,分别基于Lyapunov稳定性理论和线性矩阵不等式方法,推导出闭环系统稳定的充分条件,并给出了鲁棒最优和次优控制律的设计方法.仿真结果表明,所提出方法能实现稳定控制和有效的干扰抑制作用.

具有数据丢失的离散复杂动态网络H_∞控制

考虑到复杂动态网络节点之间的信息传输存在数据丢失和信道干扰的现象,利用Bernoulli随机序列描述数据丢失,得到离散复杂动态网络模型。在此模型基础上,基于Lyapunov稳定性理论和随机分析方法,提出了一种新的H∞控制方案,使得复杂动态网络的控制输出满足一定的H∞性能指标。该控制方案以线性矩阵不等式形式描述,给出了存在数据丢失时,离散复杂动态网络的H∞控制器设计准则。以20个节点的离散复杂动态网络为例,进行了数值仿真。仿真结果表明所设计的H∞控制器能够使耦合数据丢失的复杂动态网络均方渐近稳定,且满足一定的H∞性能指标。

非线性动态系统的模糊神经网络自适应H_∞鲁棒控制

针对非线性动态系统不稳定性,提出了一种基于模糊神经网络的H∞鲁棒直接自适应控制方法,通过设计非线性动态系统的H∞控制器,采用模糊神经网络在线学习对动态系统的建模不确定性产生的误差,可保证不确定闭环稳定并具有H∞性能,并证明了模糊神经网络H∞鲁棒直接自适应控制系统的稳定性,仿真算例也表明了该方法具有较好的抗干扰性能,鲁棒性较好.

一类变时滞复杂网络的H_∞牵制同步

研究了具有外部干扰的时变时滞复杂网络的H∞指数同步问题.采用对网络中的小部分节点实施反馈控制策略,并定义合适的控制输出,得到了被控制节点的H∞同步控制器和指数同步的H∞控制律.此外,在Lyapunov稳定性理论的基础上,基于线性不等式(LMI)方法,给出了H∞指数同步的条件及其相应的算法.与现有的设计方法相比,本文结论具有更好的保守性和可行性.最后,数值仿真实例验证了结论的有效性和可行性.

Robust dynamic surface control of flexible joint robots using recurrent neural networks

A robust neuro-adaptive controller for uncertain flexible joint robots is presented. This control scheme integrates H^infinity disturbance attenuation design and recurrent neural network adaptive control technique into the dy- namic surface control framework. Two recurrent neural networks are used to adaptively learn the uncertain functions in a flexible joint robot. Then, the effects of approximation error and filter error on the tracking performance are attenuated to a prescribed level by the embedded H-infinity controller, so that the desired H-infinity tracking performance can be achieved. Finally. simulation results verifv the effectiveness of the nronosed control scheme.

一类时滞加权动态复杂网络的牵制同步

针对一类由Lur’e系统组成的动态复杂网络,研究其同步问题.对具有大规模节点网络中的小部分节点实施反馈控制策略,从而使整个加权时滞网络的所有节点均达到同步.基于绝对稳定性理论,分别得到了保证网络达到全局同步的时滞独立及时滞依赖稳定性判据.特别地,在某些特殊情况下,只对网络中的一个节点实施牵制控制,就可使整个网络达到同步.最后,数值仿真验证了结论的有效性.

H_∞鲁棒控制下动态供应链系统牛鞭效应优化

为解决网络化制造(networked manufacturing,NM)模式下供应链系统运作中存在的不确定性扰动,运用H_∞鲁棒控制方法抑制供应链系统牛鞭效应,保障系统稳定运作.构建了由状态变量和控制变量描述的NM模式下的动态供应链时变偏差系统模型,采用线性矩阵不等式(LMI)方法获取H_∞鲁棒控制策略,并通过系统反馈控制器u_k设计,有效减小客户不确定需求引起的生产、订货和库存波动.最后,结合实例分析表明在抑制率为ξ时,本文提出的鲁棒控制策略可以有效抑制不同形式客户需求引起的牛鞭效应,实现供应链系统鲁棒镇定.

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小特征值的图谱性质,本文提出了多个受控节点选取的递归迭代算法,该算法适用于任意类型的网络.通过BA无标度网络、NW小世界网络及一些实际网络中的仿真实验表明:该算法在控制节点数较少时,能有效找到最优受控节点集.最后讨论了在复杂网络牵制控制背景下节点组重要性排序问题,提出节点组的重要性排序与受控节点的数目有关.

基于牵制控制的一类线性耦合复杂网络同步

对一类线性耦合动态复杂网络的同步问题进行研究.通过对其部分节点的牵制控制实现该复杂网络所有节点均趋于同一状态,给出该复杂网络达到全局指数同步的条件,运用李雅普诺夫稳定性理论给出严格证明.为克服实现网络同步所需耦合强度较大的弊端,利用自适应方法对网络耦合强度进行调节,在实现网络同步时获得较小的耦合强度.数值实验结果进一步验证了理论结果的有效性.

复杂动态网络的牵制同步控制

研究了复杂动态网络的牵制同步控制。首先,阐述了一个新的动态网络,这个网络具有不同的节点结构,而且每个节点都是具有相同维数的动力系统。通过设计合适的控制器,此网络的状态将指数同步到一个稳定的状态。其次,给出了一些同步准则和一个例子去验证理论结果。MATLAB仿真结果表明,在整个网络被控制到平衡点时,在网络中随机地选择两个节点施加牵制控制,甚至仅对网络中度最大的那一个节点施加牵制控制,都能使网络的状态在很短的时间内达到同步。MATLAB仿真结果与理论分析相一致。

基于随机牵制控制器的复杂网络系统的镇定

主要研究一类具有连续线性耦合节点的复杂动态网络系统的牵制控制问题,提出了一种基于随机变量的随机牵制控制方法。通过对部分节点施加带有随机变量的状态反馈牵制控制器,可以实现整个复杂网络系统的稳定。可以看出,虽然随机牵制方法不要求控制器一直作用在选定的节点上,但同样能使得复杂网络系统稳定。运用鲁棒思想首次讨论了系统耦合矩阵发生变化时所设计的随机牵制控制器的有效性问题,给出了所设计控制器仍然能保证系统的稳定性的充分条件。基于所得结果,进一步讨论了所含随机变量的期望值含有不确定性和未知时的牵制控制问题。最后通过数值仿真进一步验证了所提方法的正确性和有效性。