参数未知的统一超混沌系统自适应反同步

文章研究了参数未知的统一超混沌系统的控制与同步问题.首先基于Lyapunov稳定性理论,设计了自适应控制器,证明了该控制器可使参数未知统一超混沌系统渐近稳定于不动点.其次使用自适应反同步方法,设计了自适应同步控制器,实现了参数未知统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 自适应反同步     

统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步     

一类参数未知混沌系统的追踪控制与参数辨识

针对一类参数未知的混沌系统,提出一种追踪控制方法,基于Lyapunov稳定性理论,设计了追踪控制器和参数自适应控制律,实现了混沌系统的追踪控制和未知参数的辨识.以统一混沌系统为例进行了数值模拟,结果表明了该方法的有效性. 关键词： 混沌系统 追踪控制 参数辨识     

基于线性控制的分数阶统一混沌系统的同步

研究了分数阶统一混沌系统的同步.基于分数阶稳定性原理,提出了通过线性反馈实现分数阶统一混沌系统的同步方法.所设计的控制器为单一控制变量的线性控制器,且不需要计算反馈系数.通过对分数阶Lorenz混沌系统、Chen混沌系统和Lü混沌系统的数值模拟,证实了所提方法的有效性.     

基于追踪控制的混沌异结构同步

针对连续混沌系统，提出一种混沌异结构同步追踪控制方案.利用Lyapunov方法证明了当受控系统满足Lipchitz条件时，即可使其状态输出指数收敛到任意给定的参考信号.设计的控制器结构对不同的混沌系统具有统一的形式，可实现任意混沌系统之间的异结构同步.数值仿真进一步表明了该方法的有效性. 关键词： 混沌系统 追踪控制 同步     

混沌系统的非线性连续预测变结构控制与同步

在连续时间混沌系统的控制与同步问题统一处理的基础上,给出一种可实现两个相同或不同连续时间混沌系统的控制与同步的预测变结构控制方法.其控制器由针对对象标称非线性模型设计的连续预测控制器和针对对象不确定性设计的滑模变结构控制器组成.所提出的方案具有变结构控制鲁棒性强的优点,实现了系统对参考信号的追踪控制.数值仿真表明了本方法的有效性 关键词： 混沌同步 预测控制 滑模 变结构 鲁棒性     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

一类含参数不确定性混沌系统的自适应控制

基于Lyaponov函数,对一类含参数不确定性混沌系统,当系统的不确定性参数具有未知界时,给出了自适应控制器的设计方法和构造控制器的解析式.构造混沌控制器直接代入控制器的参数化公式即可.方法简单,无需拼凑,能够使系统消除混沌并渐近稳定到任何期望的光滑轨道上.而整个设计过程无需预先知道未知参数的估计值和精确值.仿真验证了其有效性 关键词： 混沌系统 自适应混沌控制 Lyaponov函数 参数不确定性     

一个新的超混沌系统及其自适应追踪控制

通过在一个三维混沌系统中加入状态反馈控制器, 构造出一个新的四维超混沌系统. 分析表明, 随着不同参数变化该系统呈现周期、复杂周期、准周期、混沌及超混沌运动. 同时设计出模拟电子电路对该超混沌系统进行了实验验证. 最后, 设计了一个自适应追踪控制器,实现了其对各种不同参考信号的单变量追踪控制.     

间歇同步分数阶统一混沌系统

根据分数阶微分方程的性质,研究了间歇控制分数阶系统的稳定性,提出了间歇控制分数阶系统的一般理论并给出了数学证明. 根据该理论设计控制器实现了分数阶统一混沌系统的间歇同步, 数值仿真验证了该理论的正确性. 关键词： 分数阶 统一混沌系统 间歇同步 稳定性     

控制与同步连续时间混沌系统的非线性反馈方法

在将连续时间混沌系统的控制与同步问题统一处理的基础上,给出了一种可实现两个相同或不同连续时间混沌系统的控制与同步的非线性状态反馈方法.该方法以著名的Lyapunov技术为基础,当目标和被控系统的状态变量都有界时,不论目标系统是处于平衡点、周期、拟周期、混沌或超混沌状态,都可使被控制系统按照目标系统给定的轨道演化,并且是大范围可控和可同步的. 关键词：     

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.     

Synchronization of chaotic Lur'e systems with delayed feedback control using deadzone nonlinearity

In this paper we present a synchronization method for chaotic Lur'e systems by constructing a new piecewise Lyapunov function. Using a delayed feedback control scheme, a delay-dependent stability criterion is derived for the synchronization of chaotic systems that are represented by Lur'e systems with deadzone nonlinearity. Based on the Lyapunov--Krasovskii functional and by using some properties of the nonlinearity, a new delay-dependent stabilization condition for synchronization is obtained via linear matrix inequality (LMI) formulation. The criterion is less conservative than existing ones, and it will be verified through a numerical example.     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

Chaos synchronization of unified chaotic systems via LMI

This Letter focuses on the master-slave synchronization problem of the unified chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to make the state of two identical unified chaotic systems asymptotically synchronized. Simulation results have illustrated the effectiveness of the proposed chaos synchronization solution.     

Liu混沌系统的非线性反馈同步控制

研究了新型混沌系统——Liu系统的同步控制问题.基于Lyapunov稳定性理论，采用非线性反馈控制方法，给出了Liu系统实现自同步的充分条件以及控制律参数的取值范围；结合参数自适应控制方法，实现了Liu混沌系统与统一混沌系统的异结构系统快速同步.数值仿真证明了该方法的有效性. 关键词： Liu混沌系统 混沌同步 非线性反馈控制 参数自适应控制     

Cascade adaptive control of uncertain unified chaotic systems

The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point. Since an adaptive controller based on dynamic compensation mechanism is employed,the exact model of the unified chaotic system is not necessarily required. By choosing appropriate controller parameters,chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.     

基于线性状态反馈的混沌系统全局控制

针对一类混沌系统,通过分析其非线性向量场的结构特征,提出了一种全局快速控制混沌的新方法.利用线性状态反馈,分离出一个稳定的独立状态变量方程,使受控的混沌系统逐渐退化为稳定的线性系统,进而完全消除非线性抖振现象.此方法可应用到Lorenz系统族或具有类似结构的新混沌系统的控制中,相应设计出一种结构简单的控制器,保证闭环系统在原点全局渐近稳定.数值算例验证了所提出方法的快捷性和正确有效性. 关键词： 混沌系统 线性状态反馈 全局稳定     

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal

This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic oscillators.