Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters

This paper investigates the adaptive synchronization in the drive-response fractional-order dynamical networks with uncertain parameters. By means of both the stability theory of fractional-order differential system and the adaptive control technique, a novel adaptive synchronization controller is developed with a more general and simpler analytical expression, which does not contain the parameters of the complex network, and effective adaptive laws of parameters. Furthermore, the very strong and conservative uniformly Lipschitz condition on the node dynamics of complex network is released. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyper-chaotic node dynamics are presented.     

Model reference adaptive synchronization of T–S fuzzy discrete chaotic systems using output tracking control

This paper presents a model reference adaptive control approach for the synchronization of a discrete-time chaotic systems using output tracking control. The reference model system is chosen using the output of master system and Takagi–Sugeno (T–S) fuzzy model is employed to represent the discrete-time chaotic slave system. Design the control input so that the controlled slave system achieves asymptotic synchronization with the reference system given that two systems start from different initial conditions, different parameters and/or different type of model. Using a gradient algorithm, the ideal controller gains which can stabilize the error equation are estimated. Simulation examples of two cases are given to demonstrate the validity of our proposed adaptive method.     

ADAPTIVE PINNING SYNCHRONIZATION OF COUPLED NEURAL NETWORKS WITH MIXED DELAYS AND VECTOR-FORM STOCHASTIC PERTURBATIONS＊

In this article,we consider the global chaotic synchronization of general coupled neural networks,in which subsystems have both discrete and distributed delays.Stochastic perturbations between subsyste...     

Global synchronization of weighted cellular neural network with time-varying coupling delays

New sufficient conditions are derived to guarantee the global synchronization of the weighted cellular neural network with multiple time delays. Based on Lyapunov theory, this paper proposes an adaptive feedback controlling method to identify the exact topology of a rather general weighted cellular neural network system with time-varying delays and then considers the synchronization of the neural network with different nodes dynamics. The parameters in this paper are very few and experiments show that the methods presented in this paper are of high application in global synchronization.     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach

In this paper, the robust synchronization problem for a class of stochastic delayed complex networks with switching topology and unmodeled dynamics is investigated by using the adaptive control scheme. Different from some existing uncertain complex network models, the uncertain terms in the complex networks are only needed to be bounded. Based on the stability theory of stochastic delayed differential equation, a novel adaptive controller which ensures that all the nodes in the complex networks robustly synchronize with the target node is derived. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

Adaptive cluster synchronization in networks with time-varying and distributed coupling delays

This paper studies the adaptive cluster synchronization of a generalized linearly coupled network with time-varying delay and distributed delays. This network includes nonidentical nodes displaying different local dynamical behaviors, while for each cluster of that network the internal dynamics is uniform (such as chaotic, periodic, or stable behavior). In particular, the generalized coupling matrix of this network can be asymmetric and weighted. Two different adaptive laws of time-varying coupling strength and a linear feedback control are designed to achieve the cluster synchronization of this network. Some sufficient conditions to ensure the cluster synchronization are obtained by using the invariant principle of functional differential equations and linear matrix inequality (LMI). Numerical simulations verify the efficiency of our proposed adaptive control method.     

关于耦合网络间同步控制的一个注记

本文旨在研究具有相互作用的两个网络间的同步及其控制问题,从理论上我们证明了通过选择适当的控制项,两个网络可以达到同步．文中没有限制两个网络具有相同的动力学,针对两个网络的拓扑结构和网络问的作用矩阵,我们提出了两种自适应同步格式,最后通过数值算例来阐述我们得到的理论结果．     

Impulsive synchronization of time-varying dynamical network

Synchronization of time-varying dynamical network is investigated via impulsive control. Based on the Lyapunov function method and stability theory of impulsive differential equation, a synchronization criterion with respect to the system parameters and the impulsive gains and intervals is analytically derived. Further, an adaptive strategy is introduced for designing unified impulsive controllers, with a corresponding synchronization criterion derived. In this proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is provided and evaluated. The derived theoretical results are illustrated to be effective by several numerical examples.     

Cluster synchronization in colored community network with different order node dynamics

In this paper, a colored community network model with different order nodes dynamics is introduced for the first time. The color of nodes or edges are assumed to be identical if they belong to the same community and nonidentical if they belong to different communities. The color of edges between any pair of communities are assumed to be identical if they connect the same pair of communities and nonidentical if they connect different pair of communities. Further, the order of the node dynamics in different communities can be totally different. Firstly, based on the Lyapunov stability theory, adaptive feedback controllers are designed for achieving cluster synchronization. Secondly, periodically intermittent controllers are designed for achieving cluster synchronization and the synchronization conditions are derived by using mathematical induction method and the analysis technique. Finally, several numerical examples are provided to illustrate the effectiveness of the derived theoretical results.     

Lag projective synchronization of a class of complex network constituted nodes with chaotic behavior

In this paper, a method of the lag projective synchronization of a class of complex network constituted nodes with chaotic behavior is proposed. Discrete chaotic systems are taken as nodes to constitute a complex network and the topological structure of the network can be arbitrary. Considering that the lag effect between network node and chaos signal of target system, the control input of the network and the identification law of adjustment parameters are designed based on Lyapunov theorem. The synchronization criteria are easily verified.     

Projective synchronization with different scale factors in a driven–response complex network and its application in image encryption

We study projective (anticipatory, exact and lag) synchronization of time-delayed chaotic systems in a driven–response complex network (DRCN), where the nodes are not partially linear and the scale factors are different from each other. Two synchronization criteria are presented; the first is easy to satisfy with simple limitation and the second relaxes the previous limitation and can be executed only by adding a simple linear feedback control to every node. As a special case, projective synchronization in a DRCN without time delay is analyzed by using a different method. The corresponding synchronization criterion is given, which can be realized by adopting single-node adaptive control. This paper extends previous work, where the nodes of the DRCN are partially linear, there is limitation of the coupling matrix or the scale factors of the nodes are all equal. Numerical examples are given to demonstrate the effectiveness of the proposed synchronization criteria. Due to the complexity of the different scale factors, we select the chaotic data from the DRCN presented in this paper and apply the data selected in image encryption. Simulation results show that our method is efficient with a large key space, high sensitivity to initial conditions and high speed.     

Projective lag synchronization of the general complex dynamical networks with distinct nodes

In this paper, projective lag synchronization of the general complex dynamical networks with different nodes is investigated. Combining Barbalat’s lemma with adaptive control technique, the adaptive feedback controllers are constructed to achieve projective lag synchronization between the dynamical network with diverse nodes and arbitrary desired trajectory. The presented synchronization method can be applied to any complex networks. It is discovered that the update gains, the time delay, the network size and the network topology have influence on the synchronization effect. Furthermore, projective lag synchronization of the dynamical networks can still be efficiently realized in presence of noise and parameter perturbations. Corresponding numerical simulations are performed to validate the effectiveness and robustness of the proposed synchronization scheme.     

Adaptive coupled synchronization among multi-Lorenz systems family

In this paper, the adaptive synchronization method of coupled system is proposed for multi-Lorenz systems family. This method can avoid estimating the value of coupling coefficient. Strict theoretical proofs are given. And we derived a sufficient condition of synchronization for a general unidirectional coupling ring network with N identical Lorenz systems. The network is coupled through the first state variable of each equation. In fact, the whole unidirectional coupling network will synchronize by adding only one adaptive feedback gain equation. Numerical simulations show the effectiveness of the methods.     

Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems

Based on the Lyapunov stability and adaptive synchronization theory, optimization design of adaptive controllers and parameter observers with controllable gain coefficient are investigated in detail. The linear errors of corresponding variables and parameters are used to construct different appropriate positive Lyapunov functions V and the parameter observers and adaptive controllers are approached analytically by simplifying the differential inequality dV/dt?0. Particularly, an optional gain coefficient is selected in the parameter observers and positive Lyapunov function, which decides the transient period to identify the unknown parameters and reach synchronization. The scheme is used to study the synchronization of two non-identical hyperchaotic Rössler systems. The theoretical and numerical results confirm that the four unknown parameters in the drive system are estimated exactly and the two hyperchaotic systems reach complete synchronization when the controllers and parameter observers work on the driven system. To confirm the model independence of this scheme, an alternative hyperchaotic system is investigated, whereby the results confirm that the five unknown parameters are identified rapidly and exactly, and that the two hyperchaotic systems reach complete synchronization as well.     

Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of adaptive synchronization between two nearly identical chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on Lyapunov stability theory, a novel adaptive synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. The controller is simple and systemic, no parameters of the slave system are included in the controller, and, for some specific error systems, the controller can be simplified ulteriorly. New chaotic and a new hyper-chaotic systems with uncertain parameters are taken as the examples to show the effectiveness of the proposed adaptive synchronization method.     

受扰不确定混沌系统的双路组合函数投影同步

研究了具有未知参数和外界扰动的多个混沌系统之间的双路组合函数投影同步问题.首先给出了由四个混沌驱动系统和两个混沌响应系统组成的双路组合函数投影同步系统的定义,然后以Lyapunov稳定性理论和不等式变换方法为分析依据,设计了鲁棒自适应控制器和参数自适应律,使得两路同步系统中的响应系统和驱动系统按照相应的函数比例因子矩阵实现同步,并有效克服未知有界干扰和未知参数的影响.相应的理论分析和数值仿真证明了该同步方案的可行性和有效性.     

Synchronization through system interconnections

An interconnection strategy with built-in adaptive controllersis presented which achieves synchronization of scalar linearsystems: the closed-loop network forces all outputs to followthe same signal asymptotically while maintaining the open-loopcharacteristics. In the design of the output feedback controllers,no knowledge of system parameters is assumed, but each systemmust have the same poles and be high-gain-stable. The proofof the main theorem relies critically on derived systems-theoreticresults and the special system topology as a network of interconnectedsystems. The topology is explained by first solving the simplerproblem of signal synchronization.     

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive–impulsive controller and the parameters adaptive laws are designed via the discrete‐time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the well‐known delayed Lü chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. © 2014 Wiley Periodicals, Inc. Complexity 21: 43–51, 2016