标量控制下的二次自治混沌系统不确定参数估计和自适应反同步

基于Lyapunov稳定性理论,设计了一个简单的标量自适应控制器分别使具有确定和不确定参数的三维(3D)二次自治混沌系统实现反同步.此外,从驱动和响应系统间的时序列动态估计出所有不确定参数.数值仿真表明该方法的有效性和实用性.     

一类四维混沌系统切换混沌同步

构建了一类可切换的四维混沌系统，通过选择器实现这类系统间的随机切换.简要地分析了四维混沌系统平衡点的性质、混沌吸引子的相图和Lyapunov指数等特性，并设计了实现四维混沌系统切换的实际电路.利用非线性反馈控制方法实现了这类系统与其中某个系统之间的切换混沌同步.根据系统稳定性理论，得到了非线性反馈控制器的结构和系统达到混沌同步时反馈控制增益的取值范围. 关键词： 非线性反馈 混沌同步 四维混沌系统     

一类分数阶混沌系统的自适应同步

针对一类分数阶混沌系统的同步问题,基于分数阶系统的类Lyapunov稳定性理论,设计了一种新的自适应同步控制器以及控制增益系数自适应律.与现有结果相比,该方法具有控制器结构简单、控制代价小以及通用性强等特点,可适用于大部分典型的分数阶混沌系统.最后,数值仿真结果验证了所提方法运用于分数阶混沌系统同步研究的有效性.     

一类不确定混沌系统的观测器同步

基于降维观测器的方法实现了一类具有外部扰动的混沌系统的同步. 无需知道系统外部扰动项的任何信息，就可对驱动系统设计基于降维观测器的响应系统，从而实现了混沌系统的同步. 数值仿真表明该方法是有效的. 关键词： 混沌同步 混沌系统 观测器     

利用单模激光Lorenz系统实现异结构混沌系统混沌同步

对混沌同步问题进行了研究。设计了一种同步控制器来实现异结构混沌系统之间的混沌同步。减少了控制器的数量,仅用一个控制器就能实现这一同步控制。同时,控制器只需在目标和响应系统中提取一个易提取信号即可实现,从而大大降低了同步代价,便于实际应用。以单模激光Lorenz系统和coullet系统为例,验证了这种控制器的有效性。仿真模拟结果表明,在控制器的作用下,coullet系统所有状态变量严格地跟踪了单模激光Lorenz系统的混沌轨迹,两者迅速地达到完全同步。该设计的控制方法可用于任意混沌系统,具有一定的普适性。     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论，得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性.     

一类关联混沌系统的分时切换混沌同步

提出关联混沌系统分时切换混沌同步的思想.利用线性反馈控制方法实现一类关联混沌系统中各个子系统与其复制系统间的分时切换混沌同步.根据时变系统的稳定性理论,得到了使各子系统都能实现混沌同步的反馈控制增益的取值范围.数值仿真实验证明了理论分析的正确性和可行性. 关键词： 分时切换混沌同步 线性反馈 关联混沌系统     

扰动情况下一类混沌系统的观测器同步

研究了存在外界扰动情况下一类混沌系统的同步问题，混沌系统非线性项无需满足输出反馈形式.首先对系统进行变换得到未受扰降价混沌系统，然后基于非线性观测器的思想构造同步观测系统实现了混沌同步，通过仿真证实了该方法的有效性. 关键词： 混沌系统 同步 观测器     

利用单驱动变量实现一类混沌系统的线性和非线性广义同步

研究了一类混沌系统的线性和非线性的广义同步.对此类混沌系统,通过设计一个合适的响应系统,可以仅通过传递一个驱动变量实现系统的线性和非线性广义同步.给出了该响应系统设计的一般方法.由于只需传递一个信号,比已有方法具有更高的实用价值,理论推导和数值仿真进一步表明了该方法的有效性. 关键词： 混沌系统 广义同步 单驱动变量     

基于弹性控制器的混沌同步

利用线性输出反馈，实现了混沌系统的弹性同步，削弱了控制器本身不确定性的影响.结合linear matrix inequality工具箱，方便地得到了控制器的增益形式.仿真结果表明了研究的 意义及控制器的有效性. 关键词： 混沌系统 同步 弹性控制     

Realization of generalized synchronization between different chaotic systems via scalar controller

In this paper, a very simple generalized synchronization method between different chaotic systems is presented. Only a scalar controller is used in this method. The method of obtaining the scalar controller from chaotic systems is established. The sufficient and necessary condition of generalized synchronization is obtained from a rigorous theory, and the sufficient and necessary condition of generalized synchronization is irrelative to chaotic system itself. Theoretical analyses and simulation results show that the method established in this paper is effective.     

Synchronization of coupled dynamical chaotic networks via scalar controllers

Some scalar linear controllers, which can ensure that the states of coupled chaotic dynamical networks asymptotically synchronize each other, are derived on the basis of high gain state feedback control. Numerical simulation is given to validate the proposed theoretical result.     

Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master-slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü-Lü systems, synchronizing fractional order Chen-Chen systems and synchronizing fractional-order Lü-Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.     

Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller

<正>In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integerorder chaotic system,in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method.Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus.Moreover,three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results.Finally,results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.     

一类混沌系统的同步方法

针对一类混沌系统的特点,任意构造满足一定条件的响应系统,根据滑模控制策略得到实现两者同步的反馈控制器.在可测同步误差基础上,利用扩张状态观测器来估计驱动系统与“构造”的响应系统之间的差异,把上述反馈控制策略转变为物理可实现的控制器并实现两者的同步.以Duffing和Chua’s电路为例的仿真表明效果良好 关键词： 混沌同步 滑模控制 扩张状态观测器     

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme,where two chaotic(hyperchaotic) discretetime systems synchronize for any arbitrary scaling matrix.Specifically,each drive system state synchronizes with a linear combination of response system states.The proposed observer-based approach presents some useful features:i) it enables exact synchronization to be achieved in finite time(i.e.,dead-beat synchronization);ii) it exploits a scalar synchronizing signal;iii) it can be applied to a wide class of discrete-time chaotic(hyperchaotic) systems;iv) it includes,as a particular case,most of the synchronization types defined so far.An example is reported,which shows in detail that exact synchronization is effectively achieved in finite time,using a scalar synchronizing signal only,for any arbitrary scaling matrix.