Synchronisation for complex dynamical networks with hybrid coupling time-varying delays via pinning adaptive control

This paper is concerned with the problem of synchronisation for complex networks with hybrid coupling time delays. The control strategy consisting of adaptive control and pinning adaptive control is considered. Together with an augment Lyapunov–Krasovskii functional and using the effective mathematical techniques, several conditions are derived to guarantee a class of complex dynamical networks with hybrid coupling time-varying delays to be synchronised. Finally, some representative examples are simulated to demonstrate the effectiveness of the proposed approach.     

具有脉冲耦合复杂时滞动力网络的同步

考虑了一个具有脉冲耦合的复杂时滞动力网络的同步问题.基于脉冲时滞动力系统扩展的Halanay不等式,给出了网络同步的一个充分条件.所获结果表明,即使网络节点之间仅在一些离散时刻存在瞬时连接,网络仍然能够达到同步.进一步将所得结果应用于一个由混沌FHN神经元振子为动力节点所构成的一个无标度的动力网络,数值仿真结果表明了理...     

一种新的复杂动态网络学习控制的自适应同步算法

提出了一种新的具有未知时变参数复杂动态网络同步的自适应学习控制方法.运用重新参数化技术,设计周期时变参数的自适应学习律、常参数的更新律以及自适应控制策略确保同步误差渐近收敛.通过构造复合能量函数给出同步的一个充分条件.最后给出一个复杂网络的例子验证所提方法的有效性.     

具有量化脉冲效应的时滞混杂动态网络同步分析

研究了具有量化脉冲效应的时滞混杂动态网络的同步动力学,利用偏收缩理论和矩阵测度概念,并结合量化器的特征,提出了网络节点实现同步的一般性条件.与以往大多数基于Lyapunov稳定性方法所提出的结果不同,利用本文的方法可以消除单个节点和网络耦合中的非线性函数的限制性假设,从而降低保守性.本文突出的特征就是综合了网络节点和耦合拓扑中的多重时滞影响和脉冲行为,并且考虑了脉冲效应在网络传输中的有限通信能力问题,具有实际意义.最后,通过对Lorenz混沌系统作为网络节点的混杂动态网络进行数值模拟,验证了所得结果的有效性.     

Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling

This paper is concerned with the H_∞ performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time‐varying norm‐bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input‐delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous‐time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean‐square exponential stability of the system with an H_∞ performance. What's more, an H_∞ controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Synchronization for linear singularly perturbed complex networks with coupling delays

This paper is concerned with the synchronization problem about linear singularly perturbed complex network system with coupling delay. The sufficient delay-dependent conditions for the synchronization of the network are established by introducing an equivalent network system with the Lyapunov stability theory. These conditions, which are formulated in terms of linear matrix inequalities, can be solved efficiently by the LMI toolbox of MATLAB. A simulation example is provided to show the validity of the proposed the synchronization conditions of the whole network.     

Event-triggered sampled-data synchronization of complex networks with uncertain inner coupling and time-varying delays

This paper focuses on event-triggered sampled-data synchronization of uncertain complex networks with time-varying coupled delays. First of all, a discrete event-triggered sampled-data control scheme is adopted, which not only makes the state of the system be monitored in discrete time, but also the sampling information is effectively transmitted. The proposed event-triggered mechanism effectively prevents Zeno behavior. In addition, we also use some novel piecewise time-dependent Lyapunov–Krasovskii and Wirtinger inequality to handle the time-varying delays and parameter uncertainties of complex networks. Then, synchronization criteria are given for uncertain complex networks. Finally, the simulation results show that the control scheme can significantly reduce the number of transmitted signals while maintaining the uncertain complex networks synchronization.     

Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling

In this paper, the robust synchronization control problem of an array of fuzzy cellular neural networks with uncertain stochastically coupling is investigated, which involves constant coupling, discrete time-varying delay coupling and distributed time-varying delay coupling. By using adaptive feedback control scheme and exploiting some stochastic analysis techniques, several sufficient conditions are developed to ensure the synchronization of stochastically hybrid coupled fuzzy neural networks with all admissible uncertainties in mean square. Finally, a numerical example illustrated by scale-free complex networks is provided to show the effectiveness and the applicability of the proposed method.     

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov–Krasovskii's functional and utilisation of Jensen’s inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.     

Cluster synchronisation of directed complex dynamical networks with nonidentical nodes via pinning control

In this article, we study the cluster synchronisation problem of directed complex dynamical networks through controlling some specific nodes. This method explains which nodes should be chosen as pinned candidates. Owing to the special structure of cluster network, the number of such nodes is extremely small. In our model, we consider a directed network whose nodes in different clusters are nonidentical. Then some sufficient conditions to guarantee cluster synchronisation in the coupled network are presented. Finally, numerical examples are given to verify our theoretical analysis.     

Pinning‐controlled synchronization of hybrid‐coupled complex dynamical networks with mixed time‐delays

This paper investigates the pinning‐controlled synchronization of a general complex dynamical network with hybrid coupling, which includes constant coupling, discrete‐delay coupling and distributed‐delay coupling. Furthermore, the network can be composed of coupled identical nonlinear oscillators with or without internal time‐delay. To be more consistent with the realistic networks, the internal time‐delay, the discrete time‐delay and the distributed time‐delay can be different from each other, the inner coupling matrices are not necessarily to be diagonal, and the coupling configuration matrices are not required to be symmetric or irreducible. Under some sufficient conditions, it is shown that a hybrid‐coupled complex network with or without internal time‐delay can be asymptotically pinned to a homogenous trajectory by applying adaptive control actions to a small fraction of network nodes. In particular, the paper addresses what kind of nodes should be pinned and how many nodes are needed to be pinned to achieve synchronization in a hybrid‐coupled network with fixed coupling matrices and strengths. Numerical examples are given to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

时滞耦合和非时滞耦合的奇异复杂动态网络之同步性准则

本文利用李雅普诺夫稳定性理论,对时滞耦合和非时滞耦合的奇异复杂动态网络之同步获得了一些新的充分条件.这些条件均可转化为求解一组线性矩阵不等式(LMI).在降低准则保守性的过程中,本文充分运用了矩阵函数的凸性和自由权重矩阵理论.最后给出了两个数例;与已有文献做了比较,说明本文结论的有效性,以及较低的保守性.     

Passivity-based control and synchronization of general complex dynamical networks

This paper presents some sufficient conditions for complex dynamical networks with and without coupling delays in the state to be passive. Based on the passivity property and linearization, control and synchronization of the dynamical networks are also addressed. An example and simulation results are included.     

H∞ performance analysis for discrete‐time systems with additive time‐varying delays

The problem of stability analysis for discrete time‐delay systems with additive delays is considered. New results on stability and H_∞ performance are proposed for systems with two successive delay components. By exploiting new Lyapunov–Krasovskii functionals, the proposed results have a strong practical application background in networked control systems. The criteria are expressed in the form of linear matrix inequalities, which can be readily solved by using standard numerical software. Illustrative examples are provided to show the advantage of these results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Synchronization of stochastic complex dynamical networks under self‐triggered control

In this paper, we investigate the mean square exponential synchronization of stochastic nonlinear complex dynamical networks with or without communication delays. A new self‐triggered mechanism is proposed to reduce the amount of communication while preserving the desired system's performance. Under this mechanism, the next sampling instant is dynamically determined by the latest transmitted state rather than the online detection of the event‐triggered condition. Meanwhile, we show that the inter‐execution time of self‐triggered mechanism is bounded by a strictly positive constant, and the maximal allowable delay of the underlying system is given. A simulation is provided to illustrate the effectiveness of the proposed self‐triggered scenario. Copyright © 2016 John Wiley & Sons, Ltd.     

Delay‐range‐dependent H∞ control for Markovian jump systems with mode‐dependent time delays

This paper considers mean‐square exponential stability and H_∞ control problems for Markovian jump systems (MJSs) with time delays which are time‐varying in an interval and depend on system mode. By exploiting a novel Lyapunov‐Krasovskii functional which takes into account the range of delay, and by making use of some techniques, new delay‐range‐dependent stability result and bounded real lemma for MJSs are obtained, where the introduction of the lower bound of delay is shown to be advantageous for reducing conservatism. Moreover, a sufficient condition for the solvability of the H_∞ control problem is derived in terms of linear matrix inequalities. Finally, illustrative examples are presented to show the advantage and effectiveness of the proposed approaches. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

复杂动态网络自适应有限时间同步控制

本文利用自适应控制的方法,研究了复杂动态网络有限时间同步控制问题.针对网络的耦合权重已知和耦合权重未知两种情况,分别设计了相应的自适应控制器和参数自适应律.利用有限时间稳定性定理和Lyapunov稳定性理论,证明了复杂动态网络的误差动态系统是有限时间稳定的,并给出了同步过渡时间上界的估计.最后,利用数值算例验证了本文结论的有效性.     

Improved results on synchronisation of delayed complex dynamical networks via sampled-data control

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results.