一类混沌系统的量化同步

针对信息受限的条件,研究了一类连续混沌系统的同步问题.通过一个有限容量的信道,将具有混沌形式的驱动系统和基于观测器的响应系统连接.在这种情况下,设计了有效的量化方法使得同步误差关于传输误差是输入状态稳定(ISS),同时保证传输误差是指数衰减的.从而使得混沌同步误差在信道容量有限条件下渐近趋于零.最后通过数值例子说明了本文方法的有效性.     

基于有限时间观测器的离散系统混沌同步

本文基于驱动–响应模型针对一类离散时间混沌系统提出了一种基于有限时间观测器的同步方法. 首先, 将混沌系统写成具有未知输入的线性系统形式. 随后, 给出了观测器匹配条件和强可观条件. 在观测器匹配条件的 假设下, 通过适当的状态变换, 给出了具有降维形式的有限时间观测器设计框架使得该观测器不再受到未知输入的 影响. 然后, 证明了强可观条件结合观测器匹配条件可以保证一个有限时间观测器的存在, 该观测器可以使得响应 系统达到对驱动系统的精确同步, 且达到同步所需要的时间可以任意设定, 不受观测器系统矩阵极点配置和初值条 件的影响. 最后, 给出了两个混沌系统的例子验证了所提方法的有效性.     

基于自适应无源化的蔡氏电路混沌同步

根据蔡氏电路混沌系统的特点,得出了蔡氏电路混沌驱动系统与响应系统的误差系统.根据混沌系统的同步条件,可将混沌的同步问题转化成为误差系统的稳定性问题,即使混沌同步误差系统渐近稳定以实现混沌同步控制.针对蔡氏电路混沌系统的误差系统,采用自适应无源化方法,设计了使同步误差系统渐近稳定的具有自适应功能的反馈镇定器.该控制方法实现了2个蔡氏电路混沌系统同步,仿真研究验证了该方法的有效性.     

基于有限时间观测器的混沌系统同步

根据有限时间稳定的定义,对混沌系统引入了有限时间观测器的概念,采用有限时间观测器实现混沌系统的同步,保证在给定的有限时间区间内,观测器状态与被观测系统的状态误差被限制在一个给定界内,从而达到观测系统状态的目的。利用线性矩阵不等式的方法,将观测器存在条件转化为求解系统的线性矩阵不等式。讨论了混沌系统同步的有限时间观测器的存在条件,并给出了观测器的具体设计。通过对Duffing-Holmes系统的同步仿真,验证了该方法的有效性。     

混沌和超混沌系统的自适应有限时间投影同步

在混沌系统投影同步的研究中,针对驱动-响应系统达到投影同步的时间不确定问题,提出了一种可以预先计算出同步时间,且在此时间内混沌系统实现投影同步的方法.对给定的驱动系统,构造合适的响应系统;采用自适应控制法,仅在误差系统的部分状态变量上加入自适应控制器;采用李亚普诺夫稳定性理论证明了在所采用的自适应控制律作用下,误差系统稳定同时驱动-响应系统达到有限时间投影同步.以典型的统一混沌系统和超混沌系统进行了数值仿真,结果进一步验证了上述控制方法的有效性与可行性.     

基于分数阶积分器的分数阶混沌系统状态观测器同步研究

提出了一种基于分数阶积分器的分数阶混沌系统状态观测器同步算法。通过引入一个新的变量,该变量是将驱动系统的输出信号与传输信道中干扰的和进行分数阶积分处理,然后再作为输入信号加到观测系统中,以便实现分数阶混沌系统的状态观测系统同步。然后利用Lyapunov稳定性理论和线性矩阵不等式证明了该方法的正确性。将该同步方法应用于分数阶Chen混沌系统,得出了同步误差曲线,仿真结果表明了该同步方法的有效性,最终实现了分数阶混沌系统的状态观测器同步。     

非均匀气隙永磁同步电机的有限时间混沌同步

针对非均匀气隙永磁同步电机(PMSM)混沌系统,提出一种改进的主动有限时间同步控制器.该控制器首先利用主动控制来实现动态误差系统非线性项和线性项的近似解耦,再通过有限时间稳定控制来实现驱动系统和相应系统的有限时间同步.通过仿真实验,验证了该控制器比传统的控制器具有更强的鲁棒性和快速响应能力.     

离散混沌系统的线性和非线性反馈同步法及其条件

基于离散系统稳定性理论和Pecora-Carroll混沌同步定理，研究了多变量离散混沌系统的同步问题．提出了线性和非线性反馈同步控制方法，同步系统反馈控制器由线性和非线性两部分组成，响应系统受驱动系统的所有变量驱动．通过分析误差系统的特征方程和计算响应系统的最大条件Lyapunov指数，分别导出了离散混沌系统的同步条件．将该方法应用于Henon映射系统，实现了两Henon混沌系统的同步控制．讨论了混沌系统的同步性能与控制参数的关系．基于Matlab软件的数值仿真结果表明了该方法的有效性．     

永磁同步电机系统混沌状态的主动控制

针对永磁同步电动机混沌系统的有限时间稳定控制问题,提出一种动态有源补偿的主动控制方法,使闭环系统达到近似有限时间稳定控制。首先对永磁同步电动机的数学模型进行分岔和混沌分析,判断系统进入混沌状态的条件。然后针对系统存在的混沌,通过引入奇异摄动性理论,详细地分析了闭环系统近似有限时间稳定性,提出主动控制方法,有效的解决了系统的不确定性。仿真结果表明控制方法的有效性。     

一种带时间窗口的双脉冲控制器下的忆阻振荡系统滞同步

在真实的环境中实现复杂忆阻振荡系统的同步时, 因为信息干扰及通信问题, 驱动和响应系统之间总是存在信息传输时滞, 即时滞问题具有普遍性; 另外, 脉冲控制信号的输入总是存在输入误差, 并不能实现精确地输入.本文考虑到上述实际存在的信息传输时滞和脉冲输入误差, 设计了一种比较接近真实情况的、灵活的可以带有不同时间窗口和不同控制增益的双脉冲切换控制器, 并且利用该控制器实现了两个复杂忆阻振荡系统的滞同步.基于Lyapunov稳定性理论、矩阵不等式以及脉冲控制等相关理论, 本文找出了实现一类五阶复杂忆阻振荡系统同步的条件.最后的仿真实验进一步验证了本控制方法的可行性.     

Feedback Stabilization of Singularly Perturbed Systems Under Information Constraints

The quantized feedback control for a class of singularly perturbed systems is addressed, in which the controlled system and the controller are connected via a limited capacity communication channel. First, a proper coder–decoder pair is presented such that the transmission error decays to zero exponentially under information constraints. Then, a control law in terms of linear matrix inequalities is constructed to render the resulting closed‐loop system input‐to‐state stable with regard to the transmission error. Thus the asymptotic stability of the closed‐loop system is guaranteed. It is shown that the proposed method is simple and easy to operate. Moreover, an upper bound of the small perturbation parameter for the stability of systems can be explicitly estimated with a workable computational way. Finally, two examples are presented to show the effectiveness of the proposed method.     

不确定Van der Pol混沌系统的模糊同步控制

本文研究了不确定Van der Pol混沌系统的同步问题,并进行了基于规则的模糊逻辑控制器(FLC)的控制。首先寻找主从Van der Pol混沌系统满足Lyapunov稳定性理论的条件,在此基础上建立模糊规则,设计模糊控制器,实现不确定混沌系统的同步。通过不确定VanderPol混沌系统的两组仿真结果,验证了模糊同步控制方法具有很好的鲁棒性。最后为了进一步验证该方法的有效性,本文在相同条件下,利用反馈控制的方法实现不确定主从VanderPol混沌系统的同步,然后再将此方法的仿真结果与本文的模糊同步控制方法的仿真结果在稳态误差及同步所需时间这两个方面进行对比分析。分析结果验证了本文同步方法的可行性及有效性。     

Robust synchronization of fractional-order unified chaotic systems via linear control

A new scheme for accomplishing synchronization between two fractional-order unified chaotic systems is proposed in this paper. The scheme does not require that the nonlinear dynamics of the synchronization error system must be eliminated. Moreover, the parameter of the systems does not have to be known. A controller is a linear feedback controller, which is simple in implementation. It is designed based on an LMI condition. The LMI condition guarantees that the synchronization between the slave system and the master system is achieved. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.     

Some synchronization criteria for bidirectionally-coupled chaotic systems

1IntroductionChaos synchronization,as a very important topic in thenonlinear science ,has been developed extensivelyinthelastfew years [1,2] .A wide variety of approaches [1 ~9]have been proposed for the synchronization of chaoticsystems which include linear and nonlinear feedback,adaptive control ,etc . Most of the methods mentionedabove synchronize two coupled identical chaotic systems .Accordingto the condition of coupling signal ,they can beclassified into bidirectional [3 ~5] and unidirec…     

Some synchronization criteria for bidirectionally-coupled chaotic systems

Based on the stability theory of linear time-varying continuous system,this paper investigates the synchronization of two linear bidirectionally-coupled systems.Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback.Since the trajectory of chaotic system is continuous and bounded,one can choose suitable coupled parameters to satisfy the proposed criterion.The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling.The chaotic Chen system and the generalized Lorenz-like system are taken as examples,the simulations verify the effectiveness of the proposed method.     

Chaotic laser synchronization and its application in optical fiber secure communication

In this paper, optical fiber chaotic secure communication is proposed bycoupling chaotic laser synchronous system with optical fiber propagation channel.Feedback synchronous system of chaotic semiconductor lasers is presented andsynchronous error and decoding formulae are demonstrated. Synchronization betweentwo chaotic laser systems with distributed feedback semiconductor lasers at wavelengthof 1.31 μm is simulatively achieved with almost zero synchronous error. Parametermismatch, synchronous transient response and noise effect on the system are studied.Robustness of synchronization and anti-perturbation can increase by increasing thefeedback coefficient of the system. Influence of group-velocity-dispersion and self-phasemodulation of optical fiber on chaotic laser signal and synchronization are analyzed, and itis found that group-velocity-dispersion affects pulse shape, synchronization and decoding,and limits optical fiber propagation distances, and self-phase modulation does not affectpulse shape, w     

Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications

In this study, a new controller for chaos synchronization is proposed. It consists of a state feedback controller and a robust control term using Legendre polynomials to compensate for uncertainties. The truncation error is also considered. Due to the orthogonal functions theorem, Legendre polynomials can approximate nonlinear functions with arbitrarily small approximation errors. As a result, they can replace fuzzy systems and neural networks to estimate and compensate for uncertainties in control systems. Legendre polynomials have fewer tuning parameters than fuzzy systems and neural networks. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Legendre coefficients are estimated online using the adaptation rule obtained from the stability analysis. It is assumed that the master and slave systems are the Lorenz and Chen chaotic systems, respectively. In secure communication systems, observer-based synchronization is required since only one state variable of the master system is sent through the channel. The use of observer-based synchronization to obtain other state variables is discussed. Simulation results reveal the effectiveness of the proposed approach. A comparison with a fuzzy sliding mode controller shows that the proposed controller provides a superior transient response. The problem of secure communications is explained and the controller performance in secure communications is examined.     

The problem of optimal robust Kalman state estimation via limited capacity digital communication channels

This paper considers a state estimation problem for a continuous-time uncertain system via a digital communication channel with bit-rate constraints. The estimated state must be quantized, coded and transmitted via a limited capacity digital communication channel. Optimal and suboptimal recursive coder–decoder state estimation schemes are proposed and investigated.     

Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed.