Pinning synchronization of complex delayed dynamical networks via generalized intermittent adaptive control strategy

In this paper, the problem of pinning synchronization for delayed complex directed networks via generalized intermittent adaptive control strategy is considered. First, a dynamical mode of delayed network is investigated. Second, a generalized intermittent adaptive control strategy which unified the traditional periodic intermittent control and the aperiodic case is introduced. Additionally, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria to ensure the global synchronization of delayed complex networks based on the designed control protocols are obtained. Finally, an example with numerical simulations is provided to demonstrate the validness of the theoretical results proposed scheme.     

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.     

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.     

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.     

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.     

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.     

时延复杂网络的自适应周期间歇同步控制

研究同时具有耦合时延和节点时延复杂网络的自适应周期间歇同步控制问题.运用 Lyapunov 稳定性理论,自适应控制、牵制控制和间歇控制方法,给出保证该时延复杂网络全局指数同步、且保守性更小的判定准则,并给出相应的自适应和牵制自适应间歇同步控制器设计,该控制策略对节点间的耦合强度和网络的拓扑结构等具有较强的鲁棒性.最后以时延非线性动力系统为节点对复杂网络进行数值仿真,验证了结论的正确性和有效性.     

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.     

不同节点动态的复杂网络外部同步牵制控制

研究节点动态不同的两个复杂网络的外部同步问题。运用牵制控制方法,网络模型选取节点输出线性耦合模型,基于输出控制思想,设计结构简单的牵制控制器,对响应网络中的部分节点施加输出反馈控制,使得两个复杂动态网络达到外部同步,即实现响应网络与驱动网络的渐近同步。根据李雅普诺夫稳定性理论,推出相应的同步准则,得到控制器参数选择条件。仿真时,驱动网络和响应网络分别选取Lorenz系统和Lu系统,对全局耦合网络和最近邻耦合网络两个典型网络拓扑进行仿真,验证了所提方法的有效性。     

时变复杂动力学网络的同步控制

研究时变复杂动力学网络的同步控制问题.假定网络模型中的同步轨迹及耦合配置矩阵、内部耦合矩阵的各元素均有界,当这些界值可以预估或不确定时,分别应用线性反馈控制和自适应反馈控制策略使该网络实现全局同步.通过构造Lyapunov函数,证明了对于任意初始状态的时变复杂动力学网络模型在相应的控制手段下总可以实现渐近同步.特别是设计的自适应反馈控制策略对网络的拓扑结构、节点间的耦合强度及时滞等因素表现出较强的鲁棒性.数值仿真证实了上述结论的有效性.     

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.     

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.     

Adaptive aperiodically intermittent control for pinning synchronization of directed dynamical networks

In this paper, we investigate the pinning synchronization of directed complex network with time‐varying delay under the adaptive aperiodically intermittent control. First, the model of a directed complex network is established, the interaction graph of which is not required to contain a directed spanning tree, and for which an adaptive aperiodically intermittent feedback controller is well designed. In addition, based on the Lyapunov function method and linear matrix inequality technique, several asymptotical synchronization criteria are derived via an aperiodically intermittent strategy, which is superior to the periodical scheme. Moreover, the adaptive strategy providing the exponential convergence rate and the pinning algorithm demonstrating how to select pinned nodes are presented. Finally, numerical examples are provided to illustrate the effectiveness of the derived theoretical results.     

Stability analysis and H∞ control for hybrid complex dynamical networks with coupling delays

This paper formulates and studies a model of complex dynamical networks with switching topology and coupling delays. Based on the hybrid control and Lyapunov function, the stability and robust H_∞ control of such networks with impulsive and switching effects, which have not been studied before, are addressed with some criteria derived. Examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Pinning adaptive synchronization of a general complex dynamical network

There are two challenging fundamental questions in pinning control of complex networks: (i) How many nodes should a network with fixed network structure and coupling strength be pinned to reach network synchronization? (ii) How much coupling strength should a network with fixed network structure and pinning nodes be applied to realize network synchronization? To fix these two questions, we propose a general complex dynamical network model and then further investigate its pinning adaptive synchronization. Based on this model, we attain several novel adaptive synchronization criteria which indeed give the positive answers to these two questions. That is, we provide a simply approximate formula for estimating the detailed number of pinning nodes and the magnitude of the coupling strength for a given general complex dynamical network. Here, the coupling-configuration matrix and the inner-coupling matrix are not necessarily symmetric. Moreover, our pinning adaptive controllers are rather simple compared with some traditional controllers. A Barabási-Albert network example is finally given to show the effectiveness of the proposed synchronization criteria.     

一类具有多种耦合时滞的复杂动态网络的牵制同步

针对一类由Lur'e系统组成的具有多种耦合时滞的加权复杂动态网络,研究其同步问题.只对网络中的一部分节点进行控制,从而使整个被控网络达到同步.基于绝对稳定性理论.得到了保证复杂网络实现全局同步的时滞独立判据.仿真中以蔡氏振荡器组成的复杂网络为例,验证了所提方法的有效性,且表明在某些特殊情况下,只需控制一个节点便可使整个网络达到同步.     

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.     

Robust pinning control of heterogeneous complex networks with jointly connected topologies and time-varying parametric uncertainty

The pinning/leader control problems provide the design of the leader or pinning controller in order to guide a complex network to a desired trajectory or target (synchronisation or consensus). Let a time-invariant complex network, pinning/leader control problems include the design of the leader or pinning controller gain and number of nodes to pin in order to guide a network to a desired trajectory (synchronization or consensus). Usually, lower is the number of pinned nodes larger is the pinning gain required to assess network synchronisation. On the other side, realistic application scenario of complex networks is characterised by switching topologies, time-varying node coupling strength and link weight that make hard to solve the pinning/leader control problem. Additionally, the system dynamics at nodes can be heterogeneous. In this paper, we derive robust stabilisation conditions of time-varying heterogeneous complex networks with jointly connected topologies when coupling strength and link weight interactions are affected by time-varying uncertainties. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, we formulate low computationally demanding stabilisability conditions to design a pinning/leader control gain for robust network synchronisation. The effectiveness of the proposed approach is shown by several design examples applied to a paradigmatic well-known complex network composed of heterogeneous Chua's circuits.