Adaptive synchronization of weighted complex dynamical networks with coupling time-varying delays

This Letter considers the problem of controlling a weighted complex dynamical network with coupling time-varying delay toward an assigned evolution. Adaptive controllers have been designed for nodes of the controlled network. Analytical results show that the states of the weighted dynamical network can globally asymptotically synchronize onto a desired orbit under the designed controllers. In comparison with the common linear feedback controllers, the adaptive controllers have strong robustness against asymmetric coupling matrix, time-varying weights, delays, and noise. Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed controllers.     

Structure identification and adaptive synchronization of uncertain general complex dynamical networks

This Letter proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks simultaneously. By designing effective adaptive controllers, we achieve synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, an illustrative example is presented to demonstrate the application of the theoretical results.     

Robust adaptive synchronization of general dynamical networks with multiple delays and uncertainties

In this article, a general complex dynamical network which contains multiple delays and uncertainties is introduced, which contains time-varying coupling delays, time-varying node delay, and uncertainties of both the inner- and outer-coupling matrices. A robust adaptive synchronization scheme for these general complex networks with multiple delays and uncertainties is established and raised by employing the robust adaptive control principle and the Lyapunov stability theory. We choose some suitable adaptive synchronization controllers to ensure the robust synchronization of this dynamical network. The numerical simulations of the time-delay Lorenz chaotic system as local dynamical node are provided to observe and verify the viability and productivity of the theoretical research in this paper. Compared to the achievement of previous research, the research in this paper seems quite comprehensive and universal.     

Synchronization of coupled dynamical chaotic networks via scalar controllers

Some scalar linear controllers, which can ensure that the states of coupled chaotic dynamical networks asymptotically synchronize each other, are derived on the basis of high gain state feedback control. Numerical simulation is given to validate the proposed theoretical result.     

Topology Identification of General Dynamical Network with Distributed Time Delays

Genera/dynamical networks with distributed time delays are studied. The topology of the networks are viewed as unknown parameters, which need to be identified. Some auxiliary systems （also called the network estimators） are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied in designing these network estimators. Based on linear matrix inequalities and the Lyapunov function method, the sufficient condition for the achievement of topology identification is obtained. This method can also better monitor the switching topology of dynamical networks. Illustrative examples are provided to show the effectiveness of this method.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

General methods for modified projective synchronization of hyperchaotic systems with known or unknown parameters

This work is concerned with the general methods for modified projective synchronization of hyperchaotic systems. A systematic method of active control is developed to synchronize two hyperchaotic systems with known parameters. Moreover, by combining the adaptive control and linear feedback methods, general sufficient conditions for the modified projective synchronization of identical or different chaotic systems with fully unknown or partially unknown parameters are presented. Meanwhile, the speed of parameters identification can be regulated by adjusting adaptive gain matrix. Numerical simulations verify the effectiveness of the proposed methods.     

Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback

In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal popagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment.     

Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling

This Letter investigates the global synchronization of a general complex dynamical network with non-delayed and delayed coupling. Based on Lasalle's invariance principle, adaptive global synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, a general complex dynamical network with non-delayed and delayed coupling can globally asymptotically synchronize to a given trajectory. What is more, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition and the coupling matrix is not assumed to be symmetric or irreducible. Finally, numerical simulations are presented to verify the effectiveness of the proposed synchronization criteria.     

Investigation of a Unified Chaotic System and Its Synchronization by Simulations*

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.     

融合复杂动态网络的模型参考自适应同步研究

本文根据融合复杂网络边性质的不同, 运用网络拆分的思想研究了多重边融合复杂网络的自适应同步问题.基于Lyapunov稳定性理论,采用自适应反馈控制方法,在网络节点相同和不同的情况下,分别给出了网络全局同步的准则以及相应的控制器.最后,数值仿真验证了本文方法的有效性. 关键词： 融合网络 自适应同步 Lyapunov稳定性理论     

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

<正>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 constructed 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.     

Pinning synchronization of the complex networks with non-delayed and delayed coupling

In this Letter, without assuming the symmetry of the coupling matrix, we investigate the global synchronization of the complex networks with non-delayed and delayed coupling based on the pinning controllers. Some sufficient conditions for the global synchronization by adding linear and adaptive feedback controllers to a part of nodes are obtained. Numerical examples are also provided to demonstrate the effectiveness of the theory.     

陈氏混沌系统的自适应控制

通过简单的线性状态反馈方法,分别在系统参数已知和未知的情况下研究了陈氏混沌系统的控制问题.当参数已知时,给出了反馈增益的范围;当参数未知时,设计了一自适应控制器,它克服了一般的自适应控制器中控制律不连续的缺点.通过实验仿真证明了所给方法的有效性. 关键词： 陈氏混沌系统 混沌控制 自适应控制     

Chaos control via TDFC in time-delayed systems: The harmonic balance approach

This Letter deals with the problem of designing time-delayed feedback controllers (TDFCs) to stabilize unstable equilibrium points and periodic orbits for a class of continuous time-delayed chaotic systems. Harmonic balance approach is used to select the appropriate controller parameters: delay time and feedback gain. The established theoretical results are illustrated via a case study of the well-known Logistic model.     

Robust synchronization and anti-synchronization of identical Φ6 oscillators via adaptive sliding mode control

The main goal of this paper is to propose the single input robust adaptive sliding mode controllers to accomplish synchronization and anti-synchronization between two identical Φ⁶ Duffing or Van der Pol oscillators with unmodel dynamics and external disturbances. Unlike directly eliminating the nonlinear dynamics by active control and sliding mode control in the literature, the proposed sliding mode controllers include the equivalent control part, which is only proportional to the synchronized error states, and the switching control part, where the discontinuous control functions have adaptive feedback gains. Sufficient conditions are provided based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented schemes.     

Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes.We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths.Based on the Lyapunov-Krasovskii stability theory for functional differential equations and a linear matrix inequality(LMI),some sufficient conditions for the synchronization are derived.A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.     

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.     

Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

The centrifugal flywheel governor (CFG) is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque. It has been shown that this system exhibits very rich and complex dynamics such as chaos. This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs. The effects of unknown parameters, model uncertainties and external disturbances are fully taken into account. First, it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed. Second, two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach. Finally, some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers.     

Active control of double-glazed windows. Part II: Feedback control

This paper describes an experimental investigation of an actively controlled double-glazed window. It is the second of two companion papers of which the first treated results obtained employing adaptive feedforward control. Herein, the outcome using adaptive feedback control is presented. This adaptive feedback controller has been tested in different configurations, i.e. fully and partially connected controllers. The differences between fully connected controllers with few filter coefficients and partially connected controllers with many filter coefficients are discussed. Additionally, tests with different traffic noise examples have been performed showing the ability of the actively controlled window to enhance protection against traffic noise.