Adaptive synchronization with nonlinear input

This paper considers the adaptive synchronization problem of the drive—response type chaotic systems. Using a transmitted scalar signal with an unknown time-delay, a response system is constructed. By appropriately selecting the observer gain and designing the controller, synchronization can be achieved in the presence of the drive system's disturbances and unknown parameters. A well-known chaotic system, Chua's circuit, is considered as an illustrative example to demonstrate the effectiveness of the proposed approach.     

参数未知的不同阶数混沌系统广义同步及参数估计

采用扩阶方法(使响应系统和驱动系统的维数相同)，把不同阶数混沌系统的广义同步问题转化为相同阶数混沌系统之间的广义同步，基于Lyapunov稳定性定理和自适应控制方法(用于相同阶数混沌系统的同步)，给出了自适应控制器和参数自适应律，进而实现了不同阶数混沌系统的广义同步.将该方法应用于参数未知的超Lü，Lorenz，广义Lorenz和Liu等系统之间的广义混沌同步，理论证明了该方法可以使这些系统达到渐近广义同步，并且可以辨识驱动系统和响应系统的所有参数，数值模拟进一步证明了该方法的有效性.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.     

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.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs.Based on the adaptive technique,sliding mode control method and pole assignment technique,a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs

This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller.     

不同结构混沌系统的自适应同步和反同步

针对不同结构混沌系统的同步与反同步问题进行了研究.在系统参数已知时,采用主动控制法实现混沌系统的同步与反同步,并将主动控制器的设计方法进行了推广.在参数未知时,基于Lyapunov稳定性理论和自适应控制方法,给出了自适应控制器和参数自适应律,实现了参数均未知且结构不同的驱动系统和响应系统的同步与反同步.在控制器的设计过程中,将驱动系统和响应系统进行互换,讨论了互换前后的控制器和自适应律之间的关系.数值仿真结果说明了所提出设计方法的有效性. 关键词： 混沌同步 反同步 主动控制法 自适应控制法     

通用标量混沌信号同步系统及其控制器的backstepping设计

以寻求通用标量混沌信号同步系统为目标,虚拟控制项加权为变量的严格反馈形式变参数系统为对象,采用带有调谐函数的自适应backstepping设计方法,设计了反馈控制器和相应的参数自适应律.采用所给控制器和参数自适应律,可以使通用系统的输出渐近同步于任意已知结构混沌系统的输出.理论与计算机仿真结果均证实了通用标量混沌信号同步系统及其控制器的有效性. 关键词： 混沌 严格反馈 backstepping设计 自适应控制     

具有死区非线性输入的一类不确定混沌系统的自适应控制

研究了一类具有死区非线性输入的不确定混沌系统的控制问题. 通过引入死区非线性控制项,有效的消除了实际中由于死区非线性输入的存在而引起的不良控制效果, 设计控制器过程中对系统死区模型无需任何限制条件, 同时引入扩张观测器, 从而只需要知道系统的一个状态, 就可以观测出系统待确定的未知信息. 对Duffing系统的数值仿真结果表明该控制方案是有效的. 关键词： 混沌系统 扩张观测器 死区 非线性输入     

实现连续时间标量混沌信号同步的自适应控制方法

以能大范围实现连续时间标量(超)混沌信号同步控制的非线性反馈控制器为基础,在一定的假设前提下,设计了一个自适应控制器.连续时间混沌系统的标量输出在自适应控制器的控制下,不仅能大范围同步于给定参考标量混沌信号,而且解决了非线性反馈控制器中控制系数的估计问题,又使同步控制具有一定的鲁棒性.计算机模拟结果也证实了自适应控制器的有效性. 关键词： 混沌 同步 自适应控制     

Impulsive generalized synchronization of chaotic system

In this paper, with a given manifold y= H(x) , we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this response system can achieve impulsive generalized synchronization (GS) with the drive system. Our theoretical result is supported by numerical examples.     

改进恒Lyapunov指数谱混沌系统的广义投影同步研究

对改进恒Lyapunov指数谱混沌系统的广义投影同步进行了研究.用主动控制同步法设计合适的非线性反馈控制器,通过单向耦合,实现恒指数谱混沌系统的同结构广义投影同步与异结构广义投影同步.在指出广义投影同步体系中比例因子调节作用的同时,也分析了改进恒指数谱混沌系统的全局线性调幅参数对同步体系中两个系统的作用.基于模块与复用的设计思想,详细分析并构建了广义投影同步体系中的驱动系统、控制系统与响应系统.数值仿真与电路实验仿真一致显示：调节比例因子能够获得任意比例于原驱动混沌系统输出的混沌信号;调节全局线性调幅参数,能够同时线性调整同步体系中两个系统输出的状态变量的幅值,而不影响两个系统之间的广义投影同步. 关键词： 改进恒Lyapunov指数谱混沌系统 广义投影同步 比例因子 全局线性调幅参数     

基于观测器的混沌广义同步解析设计

提出用改进的状态观测器研究混沌广义同步问题.采用解析法求得了混沌广义同步的响应系统.从状态观测器理论，得到驱动和响应系统全局渐进线性广义同步的充分条件.以超混沌R?ssler系统为例，数值研究了该同步方法.结果表明了它的有效性. 关键词： 混沌 广义同步 状态观测器 R?ssler系统     

A General Response System Control Method Based on Backstepping Design for Synchronization of Continuous Scalar Chaotic Signal

A general response system control method for synchronization of continuous scalar chaotic signal is presented. The proposed canonical genera/response system can cover most of the well-known chaotic systems. Conversely, each of these chaotic systems can Mso be used to construct the genera/response system. Furthermore, a novel controller of the proposed response system is designed based on backstepping technique, with which the output of the genera/response system and the given continuous chaotic signal can synchronize perfectly. Two numerical examples are given to illustrate the effectiveness of the proposed control method.     

Continuous-time chaotic systems： Arbitrary full-state hybrid projective synchronization via a scalar signal

Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.     

利用混沌信号驱动实现各子系统间的同步

通过对非同参数Lorenz系统驱动模型的讨论,发现对于非同参数情况,驱动系统与响应系统间严格的混沌同步关系是不存在的,同步只具有相对的意义.同时,探讨了在混沌信号驱动下稳定系统的动力学行为,说明其输出同样是混沌的.指出利用混沌信号驱动两个非同参数的子系统,可以实现两子系统之间的混沌同步输出.给出同步条件,得出的结论在实际应用中可能具有指导意义. 关键词：     

输入受限的混沌系统同步控制

在混沌系统的同步控制中, 由于混沌系统对初始状态的敏感性, 一旦两个混沌系统的状态初值偏差大, 其状态同步往往需要高幅值的控制律来达到, 这给同步控制实现带来了困难, 并且在同步控制中, 两个混沌系统的初始值通常是未知的. 本文考虑控制输入受限情况下的混沌同步控制问题, 基于符号函数的近似表示式, 将受限的控制输入建模为连续可微的光滑函数, 在每一个采样点将同步控制误差系统近似为局部最优线性模型并设计连续型线性二次型调节器(LQR)最优控制律. 为降低混沌同步控制律的幅值和维持同步系统采样时刻之间的动态, 设计了等价的离散最优控制律, 并通过调整LQR性能加权矩阵值, 确保同步控制信号不会超出其受限的上界. 最后对统一混沌模型下的三种不同混沌系统同步控制进行了仿真研究. 仿真结果验证了方法的有效性. 关键词： 统一混沌模型 符号函数 输入受限 同步控制     

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.