参数不确定混沌系统的时滞同步

当混沌系统参数不确定时,采用自适应控制方法,研究了系统间的时滞同步问题。基于Lyapunov稳定性理论,给出了同步条件,并识别出了系统的未知参数。理论推导严格证明了结果的正确性;同时,以Lorenz系统为例进行了数值仿真与说明。     

参数不确定的异时滞混沌系统的延时同步控制

构建一个新三维混沌系统,通过对系统非线性动力学特性进行分析,证实了系统的混沌特性并确定其混沌吸引子的存在,电路仿真说明了该混沌系统的物理可实现性。设计了该混沌系统的异时滞混沌系统,数值分析和电路仿真表明了异时滞混沌系统的物理可实现性。对一类参数不确定的时滞混沌系统的自适应延时同步进行讨论,以Lyapunov-Krasovskii泛函为理论基础,设计了时滞延时同步控制器,从理论上证明了当控制参数矩阵[K]满足[K-nE]为正定矩阵时,驱动系统与响应系统趋于同步,数值仿真表明了异时滞延时同步方法设计的普适性和有效性。     

随机混沌时滞神经网络的指数同步

研究受随机扰动且具有时变时滞神经网络的指数同步. 根据Lyapunov稳定性理论结合线性矩阵不等式技巧, 通过构造含时滞的状态反馈控制器, 使得受到随机扰动的驱动系统和响应系统达到指数同步, 给出了随机时滞神经网络指数同步的新判据, 最后通过仿真验证了所用方法的有效性.     

参数不确定Liu混沌系统的自适应同步

在研究单变量驱动同步的基础上,应用自适应控制理论,研究了当系统存在一个或多个不确定参数时,Liu混沌系统的同步问题.通过Lyapunov函数,推导了不同参数未知情况下误差系统渐进稳定的充分条件.仿真结果证明了自适应控制律能够快速辨识系统参数,并实现两个Liu混沌系统的状态同步.     

Lag synchronization of complex dynamical networks with randomly occurring parameter uncertainties and control packet loss via stochastic sampled-data control

ABSTRACT

This paper focuses on the lag synchronization of two general complex dynamical networks with randomly occurring parameter uncertainties and control packet loss. The randomly occurring uncertainties are adopted to reflect more realistic dynamical behaviours of complex networks that are caused by noisy environment. By introducing a Bernoulli distributed stochastic variable, the information of probabilistic time-varying delay is transformed into the deterministic time-varying delay with stochastic parameters. Sampled-data controllers with stochastically varying sampling intervals are considered and a switched system is used to describe packet dropouts in a deterministic way. Some sufficient conditions for the lag synchronization in the mean square are derived in terms of constructing an appropriate Lyapunov function and using linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the theoretical results.     

Design of controller on synchronization of chaotic neural networks with mixed time-varying delays

In this paper, the problem on synchronization is investigated for neural networks with discrete and distributed time-varying delays as well as generalized activation functions. By constructing proper Lyapunov–Krasovskii functional and employing a combination of the free-weighting matrix method, Newton–Leibniz formulation and inequality technique, the controllers are, respectively, designed to achieve the asymptotical and exponential synchronization of the addressed neural networks. The provided conditions are expressed in terms of LMIs, and are dependent on both the discrete and distributed time delays. A simulation example is given to show the effectiveness and less conservatism of the obtained conditions. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.     

Adaptive synchronization of master–slave systems with mixed neutral and discrete time‐delays and nonlinear perturbations

This paper investigates the delay‐dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time‐varying discrete time‐delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master‐slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master‐slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effectiveness of the method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

带扰动和未知参数混沌系统变量函数向量同步

研究了带有扰动和未知参数的混沌系统状态变量函数向量同步问题。分别针对驱动系统和响应系统设计出状态变量函数向量,利用自适应反馈原理和Lyapunov定理,构造出控制器,可以保证两状态变量函数向量同步。仿真结果表明该方法的有效性。     

Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters

In this paper, we investigate the robust exponential stability for stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jump parameters. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain sufficient conditions for the exponential stability of the equilibrium solution. The obtained stability criteria can be easily checked by linear matrix inequality (LMI) techniques. Finally numerical examples are provided to illustrate the obtained theoretical result.     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks 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. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.     

Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching

This paper studies the exponential synchronization problem for a class of stochastic perturbed chaotic neural networks with both Markovian jump parameters and mixed time delays. The mixed delays consist of discrete and distributed time-varying delays. At first, based on a Halanay-type inequality for stochastic differential equations, by virtue of drive-response concept and time-delay feedback control techniques, a delay-dependent sufficient condition is proposed to guarantee the exponential synchronization of two identical Markovian jumping chaotic-delayed neural networks with stochastic perturbation. Then, by utilizing the Jensen integral inequality and a novel Lemma, another delay-dependent criterion is established to achieve the globally stochastic robust synchronization. With some parameters being fixed in advance, these conditions can be solved numerically by employing the Matlab software. Finally, a numerical example with their simulations is provided to illustrate the effectiveness of the presented synchronization scheme.     

Exponential stability analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed delays

In this paper, we study a new class of stochastic Cohen-Grossberg neural networks with reaction-diffusion and mixed delays. Without the aid of nonnegative semimartingale convergence theorem, the method of variation parameter and linear matrix inequalities technique, a set of novel sufficient conditions on the exponential stability for the considered system is obtained by utilizing a new Lyapunov-Krasovskii functional, the Poincaré inequality and stochastic analysis theory. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Therefore, our results generalize and improve some earlier publications. Moreover, two numerical examples are given to show the effectiveness of the theoretical results and demonstrate that the stability criteria existed in the earlier literature fail.     

时滞神经网络双周期间歇控制滞后同步

提出了一个时滞神经网络周期间歇控制滞后同步策略,其间歇控制周期为两个不同的周期。利用Lyapunov稳定性理论,证明了时滞神经网络在此控制策略下能够实现同步,并获得了同步解全局指数稳定的充分条件。给出了一个仿真实例验证了控制方案的有效性。     

具有混合时滞的四元数神经网络全局同步性控制

本文研究了具有混合时滞的四元数神经网络的全局同步性问题. 在不要求网络的激活函数可分离为两个复数或四个实数的情况下, 通过选取合适的 Lyapunov -Krasovskii 泛函, 并运用驱动-响应同步、自由权矩阵方法和矩阵不等式技巧, 给出了网络全局同步性的充要条件, 建立了同步控制器的设计方法. 给出的同步性判据是四元数和复数两种形式的线性矩阵不等式, 同时与已有的结果进行了对比. 最后通过一个数值仿真算例验证了所得结论的有效性.     

Adaptive synchronization of uncertain coupled stochastic complex networks

In this paper, the problem of adaptive synchronization of uncertain coupled complex networks is investigated. Some controllers and adaptive laws are designed to ensure achieving synchronization of a general complex network model. In particular, synchronization of coupled stochastic networks subject to random perturbations is studied, with a referenced node introduced as the target node for synchronization. An example is simulated on delayed neural networks coupled in a small‐world network topology, which demonstrates the feasibility and effectiveness of the proposed adaptive control method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

具有未知参数的不确定分数阶Sprott-C系统的Terminal滑模同步

基于滑模控制的优良性能,探讨了利用Terminal滑模控制实现分数阶混沌系统的有限时间同步问题,给出了滑模控制实现具有未知参数和扰动的分数阶Sprott-C驱动—响应系统(阶数0<α<1)的同步结论。通过构造合适的滑动模态曲面,针对系统未知参数上界已知和未知两种情况,设计了合适的分数阶控制器和参数自适应率,结合分数阶微分方程相关理论和有限时间稳定性定理,证明了实现该系统的同步控制结论,并对未知参数和扰动上界进行了准确估计。最后选取适当参数,通过数值仿真,验证了所给结论的有效性和可行性。     

Adaptive synchronization of different kinds of chaotic neural networks

The purpose of the paper is to present an adaptive control method for the synchronization of different classes of chaotic neural networks. A new sufficient condition for the global synchronization of two kinds of chaotic neural networks is derived. The proposed control method is efficient for implementing the synchronization when the parameters of the drive system are different from those of the response system. A numerical example is used to demonstrate the validity of the proposed method and the obtained result.     

神经网络的滞后同步及其在保密通信中的应用*

针对参数不同、结构不同的带离散与分布时滞的混沌神经网络进行了研究。基于Lyapunov稳定性理论,提出了自适应滞后同步的控制方法,最后达到同步。仿真示例验证了本方案的有效性;同时应用于计算机保密通信可以掩盖有用信号,且可以无失真恢复有用信号。     

Adaptive synchronization of different kinds of chaotic neural networks

The purpose of the paper is to present an adaptive control method for the synchronization of different classes of chaotic neural networks. A new sufficient condition for the global synchronization of two kinds of chaotic neural networks is derived. The proposed control method is efficient for implementing the synchronization when the parameters of the drive system are different from those of the response system. A numerical example is used to demonstrate the validity of the proposed method and the obtained result.     

一类参数不确定混沌系统的广义同步

针对一类混沌系统,研究了参数未知的混沌系统的广义同步．基于lyapunov稳定性定理和自适应控制方法,给出了自适应控制器和参数自适应律的解析表达式．将该方法应用于参数未知的新混沌系统,理论证明了该方法可以使新混沌系统达到渐近的广义同步,并且可以辨识出系统的未知参数．数值模拟进一步证明了该方法的有效性．