奇异Lur'e网络的自适应牵制聚类同步控制

本文分别研究了由奇异和非奇异Lur''e系统组成的具有多种耦合方式时滞复杂动态网络的聚类同步问题. 通过设计一类牵制反馈控制器, 仅控制当前聚类中与其它聚类有直接连接的Lur''e系统, 从而有效减少控制器个数同时降低控制成本. 考虑到网络具有多种耦合方式, 本文合理构造Lyapunov 泛函, 并有效利用扇形条件、非线性函数类概念、S过程以及Lyapunov 稳定性定理等方法, 分别给出奇异和非奇异Lur''e 动态网络实现聚类同步的判定条件. 此外, 为有效节省控制成本, 针对控制强度设计一类自适应更新定律, 从而得到网络实现聚类同步的最优控制强度. 最后, 为了验证所得聚类同步判定条件和控制器的有效性, 对一类典型Lur''e网络聚类同步问题进行了数值仿真.     

Master‐slave synchronization for delayed Lur'e systems using time‐delay feedback control

This paper deals with the problem of designing delayed feedback controllers of master‐slave synchronization for Lur'e systems with time‐variant delay (0≤τ₀≤τ(t)≤τ_m). Through partitioning the intervals [0, τ₀] and [τ₀, τ_m], respectively, and choosing two augmented Lyapunov‐Krasovskii functionals(LKFs), two delay‐dependent synchronization criteria are formulated in the form of linear matrix inequalities (LMIs), in which the conservatism can be greatly reduced by thinning the partitioning of delay intervals and employing convex combination. Thus the sufficient conditions can be derived for the existence of delayed feedback controllers, and the controller gain matrices can be achieved by solving the established LMIs. Finally, three numerical examples are given to illustrate the presented synchronization schemes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A unified synchronization criterion for impulsive dynamical networks

This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named “average impulsive interval”. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.     

Robust cooperative output regulation of heterogeneous Lur'e networks

In this paper, we study robust cooperative output regulation problems for a directed network of Lur'e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneous. As is common in the context of Lur'e systems, the unknown nonlinearities are assumed to be sector bounded within one given sector. The interconnection graph among these agents is assumed to contain a directed spanning tree. Similar to classical output regulation problems, there is a virtual exosystem generating a reference signal in which all the agents are required to track cooperatively. Our designed distributed dynamic state/output feedback protocol makes a copy of the reference signal at each agent asymptotically, and then the robust cooperative output regulation problem becomes a robust tracking problem that can be handled by each agent via local information. It turns out that our cooperative protocols are fully distributed. Sufficient conditions on the existence of output synchronization protocols are given along with some discussions on these conditions. Finally, two simulation examples illustrate our design. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results.     

Synchronization of uncertain complex dynamical networks via adaptive control

In this paper, synchronization of an uncertain dynamical network with time‐varying delay is investigated by means of adaptive control schemes. Time delays and uncertainties exist universally in real‐world complex networks. Especially, parameters of nodes in these complex networks are usually partially or completely uncertain. Considering the networks with unknown or partially known nodes, we design adaptive controllers for the corresponding complex dynamical networks, respectively. Several criteria guaranteeing synchronization of such systems are established by employing the Lyapunov stability theorem. Analytical and numerical results show that the proposed controllers have high robustness against parameter variations including network topologies, coupling structures, and strength. Copyright © 2008 John Wiley & Sons, Ltd.     

On Designing Time‐delay Feedback Controller for Master‐Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing a time‐delay output feedback controller for master‐slave synchronization of Lur'e systems. The time delay is divided into two intervals and different energy functions are defined in each interval, which together provide a new Lyapunov–Krasovskii functional and derive a new delay‐dependent synchronization criterion. A sufficient condition for the existence of such a feedback controller is given, and an explicit expression of such a controller is also achieved. These algorithms are formulated in terms of linear matrix inequalities that can be solved easily. Chua's circuit is used to illustrate the effectiveness of the design method.     

Exponential synchronization of impulsive complex networks with output coupling

This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Global exponential synchronization of stochastic switching networks with time‐varying delay

This paper is concerned with the global exponential synchronization of stochastic delayed switching networks via hybrid control. The network under investigation is quite general to reflect the reality, where the network topology consists of r modes and switches from one mode to another according to a Markovian chain with known transition probability. Parameter uncertainties, time varying delay and stochastic disturbances are all taken into account in this study. Based on the Lyapunov functional method and stochastic analysis techniques, some new criteria for the global robust synchronization via hybrid control are established. Finally, one example with numerical simulation is given for illustration. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

This paper explores the stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays (ICSNMT). The coupling structure can be nonlinear and the time‐varying delays in which can be different, which can well describe more realistic networks. In order to describe this multicoupling structure, we build ICSNMT on a digraph with multiple arcs. Two cases are discussed, ie, (i) the continuous dynamics is stable and (ii) the impulsive dynamics is stable. Then, by means of impulsive differential inequalities with multiple delays and weighted Lyapunov functions method where the weights are closely linked to the network's topological structure, some stability criteria are established. Then, the theoretical results are illustrated by examples of bidirectional associative memory neural networks and coupled modified Chua's circuits, respectively. The numerical simulations are also carried out to demonstrate the effectiveness and feasibility of our theoretical findings.     

Stochastic synchronization of delayed multiagent networks with intermittent communications: An impulsive framework

This paper investigates the stochastic synchronization problem of delayed multiagent networks with intermittent communications. Two kinds of impulsive effects are taken into account, ie, impulsive controller (positive impulsive effect) and impulsive disturbance (negative impulsive effect). Impulsive controller allows the synchronization to be realized and requires only state information exchange at discrete time instants such that the communication cost of bandwidth is reduced. Meanwhile, impulsive disturbance is inevitable in most of practical systems and therefore is taken into consideration at discrete time instants. Sufficient conditions for synchronization are given in terms of the graph topology, the control coupling gains, and the individual agent dynamics parameters, which indicates that synchronization can be realized if the impulsive effects coefficients and communication rate are suitably selected. Simulation results verify the effectiveness of the proposed synchronization protocol.     

Synchronization of singular switched complex networks via impulsive control with all nonsynchronized subnetworks

This paper studies impulsive synchronization of a class of nonlinear singular switched complex networks (SSCNs). With the aid of discretized Lyapunov function method and the matrix generalized inverse technique, an impulsive controller is designed, which works on both the slow and the fast state variables to synchronize SSCNs at impulsive instant. Based on the designed controller, it is shown that the synchronization of SSCNs is achieved in two cases: all subnetworks that are not self‐synchronized and all subnetworks that are self‐synchronized. Moreover, an example is given to validate the effectiveness of the proposed controller.     

Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect

This paper investigates the problem of the dynamical behaviours of a class of complex-valued neural networks with mixed time delays and impulsive effect. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for assuring the exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and mathematical induction method. The obtained results generalise the existing ones. Finally, two numerical examples with simulations are given to demonstrate the feasibility of the proposed results.     

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.     

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.     

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.     

Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

This paper addresses Master–Slave synchronization for some memristor‐based fractional‐order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional‐order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann‐Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set‐valued map, differential inclusions theory, fractional Barbalat's lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.     

事件触发下马尔可夫跳跃神经网络的随机同步

本文研究了事件触发机制下带有随机噪声的马尔可夫跳跃神经网络的随机同步问题.为了更有效地降低数据传输量和节约网络资源,本文采用了一种事件触发控制.当传输误差和状态误差满足触发条件时,数据才能够被传输,使得主从系统可以在有限的资源和带宽下实现同步.通过构建新的Lyapunov泛函,以及使用广义Dynkin公式和不等式分析方...     

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.     

Homogeneous control law design for output synchronization of networked Lur'e‐type systems with disturbances

In this paper, the homogeneous distributed control law is proposed such that the outputs of the networked Lur'e systems with disturbances are synchronized. A novel adaptive distributed state‐based disturbance compensator technique is utilized such that the disturbances can be offset asymptotically. The design of the distributed compensator is constructive in that some particular functions of the states of the Lur'e systems are included. The functions always exist for the considered Lur'e‐type system. Moreover, a theorem of networked Lur'e systems subject to disturbances is first presented to show the boundedness of the states of the closed‐loop system. Then, the synchronization is shown by the incremental passivity theory and graph theory. Finally, the effectiveness of the current method is illustrated by the networked Van der Pol oscillators with disturbances.