参数未知分段混沌系统的时滞广义投影同步

研究了一类参数未知的分段修正Lorenz-Stenflo混沌系统的时滞广义投影同步问题. 基于Lyapunov稳定性理论, 提出了自适应非线性反馈控制器设计及其参数更新律, 能够根据误差大小和状态变化自动调节反馈系数, 在辨识出实时驱动系统和时滞响应系统多组未知参数的同时, 实现所有状态变量的不同比例广义投影同步. 仿真结果表明了该方法对分段混沌系统时滞同步的现实可行性和有效性. 关键词： 广义投影同步 分段混沌系统 时滞 参数未知     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

基于LMI的参数未知时变时滞混沌系统模糊自适应H_∞同步

考虑一类结构相同但驱动系统参数未知的两个时变时滞混沌系统同步问题,提出了基于T-S模糊模型的模糊自适应H∞同步方法.基于Lyapunov稳定性理论和线性矩阵不等式技术,给出了驱动系统参数未知时变时滞混沌系统同步的充分条件.仿真结果表明了所提方法的有效性.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

带未知扰动的多涡卷混沌系统修正函数时滞投影同步

研究了带有未知外部扰动的不同多涡卷混沌系统修正函数时滞投影同步问题. 基于Lyapunov稳定性理论, 采用模糊自适应控制的方法设计自适应同步控制器及参数的更新规则. 该控制器在实现混沌系统修正函数时滞投影同步的同时对外界扰动的变化能保持较好的稳定性. 数值仿真的结果进一步验证了该方法的有效性.     

带有控制输入扰动和死区的混沌系统自适应模糊控制

针对带有非线性输入和控制增益矩阵扰动的未知时变时滞混沌系统,提出了一种自适应模糊变结构控制方法.设计的控制器可以保证跟踪误差收敛到原点的可调邻域内,并且闭环系统所有信号有界.该方法对系统扰动的变化能保持较好的鲁棒性.最后以多卷波混沌系统为例的仿真实验进一步验证了该方法的有效性.     

基于混沌蚂蚁群算法的Lorenz混沌系统的参数估计

通过构造一个适当的适应度函数，首先将混沌系统的参数估计问题转化为参数的寻优问题，之后利用混沌蚂蚁群算法的全局优化搜索能力对这个问题进行求解.以典型的Lorenz混沌系统为例进行了数值模拟.实验数值仿真结果表明，使用该方法可以对混沌系统的未知参数进行有效地估计.     

Lorenz混沌系统的参数辨识与控制

把观测器思想用于系统中未知参数的辨识,对Lorenz混沌系统中的未知参数进行了辨识研究,提出未知参数辨识观测器的概念,数值结果表明若未知参数为常数或缓慢变化的信号本文方法都能给出很好的辨识结果.随后,把辨识和控制问题综合起来考虑,提出改进Lorenz混沌的控制方法,数值仿真表明了该方法的有效性 关键词： Lorenz混沌系统 参数辨识 非线性反馈控制     

基于无记忆状态观测器的多时滞不确定非线性系统的自适应控制

针对一类多时滞不确定非线性系统,研究了基于无记忆状态观测器的自适应控制问题.时滞状态扰动的上界未知,在控制中通过自适应律估计未知参数,并利用估计值设计了不依赖于时滞的无记忆状态观测器和控制器,基于Lyapunov-Krasovskii函数证明了观测误差渐近收敛到零.最后仿真结果说明了该方法的有效性.     

离散混沌系统的最小能量控制

对于离散混沌系统的最小能量控制问题，提出了一种框架性方法，该方法具有通用性.首先，设计一个二次目标函数，同时把混沌系统分解为线性部分和非线性部分两项和.然后，提出了求解非线性最优控制问题的两级算法：第一级对混沌系统中的非线性部分进行预估，以使原系统变为带有常数项的线性系统；第二级用动态规划求解一个非典型线性二次最优控制问题，并把解返回第一级，第一级根据第二级的解对非线性部分重新预估.这样通过两级间不断的信息交换，最终得到混沌系统的最优控制律.该方法不仅实现了对混沌系统的控制，而且在整个控制过程中消耗的控制能量最小. 关键词： 混沌系统 两级优化 最优控制     

Time-delayed chameleon: Analysis,synchronization and FPGA implementation

In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware–software co-simulation and the results are presented.     

Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.     

Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters

In this Letter, synchronization of a class of chaotic neural networks with known or unknown parameters is investigated. By combing the adaptive control and linear feedback with update law, a simple, analytical, and rigorous adaptive feedback scheme is derived to achieve synchronization of two coupled neural networks with time-varying delay based on the invariant principle of functional differential equations and parameter identification. With this method, parameter identification and synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis.     

Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.     

一种新的参数估计方法及其在混沌信号盲分离中的应用

为了有效地估计非线性映射中的参数,本文采用一种容积准则近似该映射的加权积分函数. 基于由状态空间模型建模的参数,提出了一种新的参数估计方法. 混沌信号的盲分离是一种具有挑战性的参数估计问题.将新的参数估计方法应用在该问题上, 实现混沌信号的有效重构.仿真结果表明该算法具有较快的收敛速度和较高的数值精度, 并能有效地分离原始混沌信号.     

Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system

In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Synchronization and parameter identification of one class of realistic chaotic circuit

In this paper, the synchronization and the parameter identification of the chaotic Pikovsky--Rabinovich (PR) circuits are investigated. The linear error of the second corresponding variables is used to change the driven chaotic PR circuit, and the complete synchronization of the two identical chaotic PR circuits is realized with feedback intensity k increasing to a certain threshold. The Lyapunov exponents of the chaotic PR circuits are calculated by using different feedback intensities and our results are confirmed. The case where the two chaotic PR circuits are not identical is also investigated. A general positive Lyapunov function V, which consists of all the errors of the corresponding variables and parameters and changeable gain coefficient, is constructed by using the Lyapunov stability theory to study the parameter identification and complete synchronization of two non-identical chaotic circuits. The controllers and the parameter observers could be obtained analytically only by simplifying the criterion dV/dt<0 (differential coefficient of Lyapunov function V with respect to time is negative). It is confirmed that the two non-identical chaotic PR circuits could still reach complete synchronization and all the unknown parameters in the drive system are estimated exactly within a short transient period.