Robust chaos synchronization using input-to-state stable control

In this paper, we propose a new input-to-state stable (ISS) synchronization method for a general class of chaotic systems with disturbances. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the ISS synchronization controller is presented not only to guarantee the asymptotic synchronization but also to achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation studies are presented to demonstrate the effectiveness of the proposed ISS synchronization scheme.     

基于Min-Max方法的混沌系统采样同步控制研究

针对含有扰动的混沌系统, 设计采样同步控制器, 利用输入时滞法将含有采样同步控制器的混杂系统转换为具有输入时滞的连续系统. 并考虑对系统影响最坏的干扰程度, 在该种情况下, 基于线性矩阵不等式(LMI)技术和min-max鲁棒控制方法, 给出了使误差系统稳定的充分条件, 确保混沌系统在所容许的扰动下均能实现完全同步. 仿真结果说明所设计的采样同步控制方案具有很强的鲁棒性, 适合应用于保密通信系统中. 关键词： 混沌同步 采样控制 min-max方法 输入时滞     

Synchronization Scheme for Uncertain Chaotic Systems via RBF Neural Network

A sliding mode adaptive synchronization controller is presented with a neural network of radial basis function （RBF） for two chaotic systems. The uncertainty of the synchronization error system is approximated by the RBF neural network. The synchronization controller is given based on the output of the RBF neural network. The proposed controller can make the synchronization error convergent to zero in 5s and can overcome disruption of the uncertainty of the system and the exterior disturbance. Finally, an example is given to illustrate the effectiveness of the proposed synchronization control method.     

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization (FPS) in drive-response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.     

A novel robust proportional-integral （PI） adaptive observer design for chaos synchronization

In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.     

Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs). Each cell in an FCNN contains fuzzy operating abilities. The entire network is governed by cellular computing laws. The design of FCNNs is based on fuzzy local rules. In this paper, a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated. Mixed delays include discrete time-varying delays and unbounded distributed delays. A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network. By constructing the Lyapunov–Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs. The controller can be easily obtained by solving the derived LMIs. A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.     

Exponential synchronization of stochastic impulsive perturbed chaotic Lur''e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

H∞ synchronization of chaotic systems using output feedback control design

This article investigates the H_∞ synchronization problem for a general class of chaotic systems. Based on Lyapunov theory, linear matrix inequality (LMI) and linear matrix equality (LME) formulation, the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an H_∞-norm constraint. Two illustrative examples are provided to demonstrate the effectiveness of the developed theoretical results.     

Master-slave synchronization of Lur'e systems with sector and slope restricted nonlinearities

This Letter presents a synchronization method for Lur'e systems with sector and slope restricted nonlinearities. A static error feedback controller based on the Lyapunov stability theory is proposed for asymptotic synchronization. The Lyapunov function candidate is chosen as a quadratic form of the error states and nonlinear functions of the systems. The nonlinearities are expressed as convex combinations of sector and slope bounds by using convex properties of the nonlinear function so that equality constraints are converted into inequality constraints. Then, the feedback gain matrix is derived through a linear matrix inequality (LMI) formulation. Finally, a numerical example shows the effectiveness of the proposed method.     

Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach

This Letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. H^∞ and sliding mode control are combined to construct a robust tracking controller. The incorporated H^∞ controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated.     

Non-fragile synchronization of genetic regulatory networks with randomly occurring controller gain fluctuation

This study examines the non-fragile synchronization of genetic regulatory networks (GRNs) with time-varying delays. Genetic regulatory network is formulated and sufficient conditions are derived to guarantee its synchronization based on master-slave system approach. The non-fragile observer based feedback controller gains are assumed to have the random fluctuations, two different types of uncertainties which perturb the gains are taken into account. By constructing a suitable Lyapunov-Krasovskii stability theory together with linear matrix inequality (LMI) approach we derived the delay-dependent criteria to ensure the asymptotic stability of the error system, which guarantees the master system synchronize with the slave system. The expressions for the non-fragile controller can be obtained by solving a set of LMIs using standard softwares. Finally, some numerical examples are included to show that the proposed method is less conservative than existing ones.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.     

Robust projective lag synchronization in drive-response dynamical networks via adaptive control

This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.     

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme (the so-called dual-stage impulsive control), some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.     

Robust chaos synchronization based on adaptive fuzzy delayed feedback ${\bf{\mathcal{H}}}_{\bf{\infty}}$ control

In this paper, we propose a new adaptive H_￥\mathcal H_\infty synchronization strategy, called an adaptive fuzzy delayed feedback H_￥\mathcal H_\infty synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback H_￥\mathcal H_\infty control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H_￥\mathcal{H}_{\infty } performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.     

相空间压缩实现时空混沌系统的广义同步

提出了一种通过相空间压缩实现时空混沌系统广义同步的方法. 以Fitzhugh-Nagumo反应扩散时空混沌系统为例,仿真模拟说明了该方法的有效性与实用性. 通过研究有界噪声作用下该系统的同步效果,表明这种同步方法具有较强的抗干扰能力. 此方法可以实现任意时空混沌系统的广义同步,具有普适性. 同步控制器结构简单、易于应用. 关键词： 时空混沌 广义同步 相空间压缩     

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality(LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.     

Finite-Time Pinning Synchronization Control for T-S Fuzzy Discrete Complex Networks with Time-Varying Delays via Adaptive Event-Triggered Approach

This paper is concerned with the adaptive event-triggered finite-time pinning synchronization control problem for T-S fuzzy discrete complex networks (TSFDCNs) with time-varying delays. In order to accurately describe discrete dynamical behaviors, we build a general model of discrete complex networks via T-S fuzzy rules, which extends a continuous-time model in existing results. Based on an adaptive threshold and measurement errors, a discrete adaptive event-triggered approach (AETA) is introduced to govern signal transmission. With the hope of improving the resource utilization and reducing the update frequency, an event-based fuzzy pinning feedback control strategy is designed to control a small fraction of network nodes. Furthermore, by new Lyapunov–Krasovskii functionals and the finite-time analysis method, sufficient criteria are provided to guarantee the finite-time bounded stability of the closed-loop error system. Under an optimization condition and linear matrix inequality (LMI) constraints, the desired controller parameters with respect to minimum finite time are derived. Finally, several numerical examples are conducted to show the effectiveness of obtained theoretical results. For the same system, the average triggering rate of AETA is significantly lower than existing event-triggered mechanisms and the convergence rate of synchronization errors is also superior to other control strategies.     

Anti-synchronization of Time-delayed Chaotic Neural Networks Based on Adaptive Control

This paper investigates the adaptive anti-synchronization problem for time-delayed chaotic neural networks with unknown parameters. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) approach, the adaptive anti-synchronization controller is designed and an analytic expression of the controller with its adaptive laws of unknown parameters is shown. The proposed controller can be obtained by solving the LMI problem. An illustrative example is given to demonstrate the effectiveness of the proposed method.