No-chattering sliding mode control in a class of fractional-order chaotic systems

A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.     

A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS

We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.     

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.     

Chaos detection and control in a typical power system

In this paper, a new chaotic system is introduced. The proposed system is a conventional power network that demonstrates a chaotic behavior under special operating conditions. Some features such as Lyapunov exponents and a strange attractor show the chaotic behavior of the system, which decreases the system performance. Two different controllers are proposed to control the chaotic system. The first one is a nonlinear conventional controller that is simple and easy to construct, but the second one is developed based on the finite time control theory and optimized for faster control. A MATLAB-based simulation verifies the results.     

基于高斯伪谱方法的混沌系统最优控制

针对混沌系统最优控制问题,提出一种基于高斯伪谱方法的数值求解新算法. 首先在勒让德-高斯点上构造Lagrange插值多项式并近似表示混沌系统最优控制中的状态变量和控制变量;接着将连续空间的最优控制问题转化为非线性规划问题;然后通过序列二次规划（SQP）算法获得最优解;最后对三个典型混沌系统的仿真实验结果表明,新方法能有效和快速地实现混沌系统的最优控制. 关键词： 混沌系统 最优控制 高斯伪谱法 非线性规划     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法.以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真.研究表明了该同步方法的有效性。     

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.     

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear R?ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R?ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.     

广义Hénon混沌系统的自适应双模控制与同步

提出一种广义Hénon映射的自适应双模控制与同步方法.广义Hénon映射的混沌吸引子比Hénon映射的混沌吸引子更复杂,控制与同步困难,对于保密通信来说具有更高的安全性.该方法采用自适应双模控制,实现了广义Hénon映射的追踪控制与同步,提高了受控系统抑制参数摄动和随机扰动的能力,改善系统的鲁棒性.仿真结果验证了该方法的有效性.     

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.     

Chaotic transient and the improvement of system flexibility

On this work it is addressed the problem of how to exploit the dynamic behind a chaotic transient behavior to improve system performance and adaptability to many operational conditions request. The phenomena of chaotic transient is explained as due to the presence of a chaotic saddle in the phase space. Different system operation points can be associated to the set of unstable periodic orbits that exist embedded in the chaotic saddle. A classical control procedure associated with a control of chaos strategy is proposed as a methodology to quickly guide system trajectories among different operation points and to keep the system on a particular operation point. The methodology is applied on an electronic circuit system.     

单模激光Lorenz系统反同步控制研究

提出了一种实现异结构混沌系统反同步控制的方法。根据Lyapunov 稳定性理论给出控制器的结构。以单模激光Lorenz系统和Rossler系统为例,验证了这种控制器的有效性。进一步研究了不确定混沌系统的反同步,并以不确定单模激光Lorenz系统和Rossler系统为例,实现了混沌反同步控制,同时系统中不确定参数得到识别。仿真模拟结果验证了这种方法的有效性。设计的反同步控制方法可用于任意混沌系统,具有一定的普适性。     

滤波法控制混沌的电路实验

以三维自治混沌系统为例,介绍了利用低通滤波器控制混沌的方法.利用低通滤波器在通带内具有相移特性,将电路中的某一变量经过低通滤波后再反馈到混沌系统中来实现混沌控制,通过改变电路元件的参量,可以将混沌控制到不同的周期轨道.     

Decentralized state-feedback chaotification method of discrete Takagi-Sugeno fuzzy systems

A new chaotification method is proposed for making an arbitrarily given discrete Takagi-Sugeno (TS) fuzzy system chaotic. Based on a given discrete TS fuzzy system, the new chaotification method uses the decentralized state-feedback control and the continuous sawtooth function, instead of the modulo operation, to construct a chaotic nonlinear system,which can generate discrete chaos with the arbitrarily desired amplitude bound. We apply the improved Marotto theorem to mathematically prove that the controlled system is chaotic in the sense of Li and Yorke. In particular, an explicit formula for the computation of chaotification parameters is obtained. A numerical example is used to illustrate the theoretical results.     

Analysis,synchronization and circuit design of a novel butterfly attractor

This research paper introduces a novel three-dimensional autonomous system, whose dynamics support periodic and chaotic butterfly attractors as certain parameters vary. A special case of this system, exhibiting reflectional symmetry, is amenable to analytical and numerical analysis. Qualitative properties of the new chaotic system are discussed in detail. Adaptive control laws are derived to achieve global chaotic synchronization of the new chaotic system with unknown parameters. Furthermore, a novel electronic circuit realization of the new chaotic system is presented, examined and realized using Orcad-PSpice program and physical components. The proposed novel butterfly chaotic attractor is very useful for the deliberate generation of chaos in applications.     

分数阶Liu混沌系统及其电路实验的研究与控制

基于波特图的频域近似方法,研究了分数阶Liu混沌系统,并设计了一种树形电路单元来实现分数阶Liu混沌系统,通过对2.7阶Liu混沌系统的电路仿真和实验,以及α=0.8—0.1(步长0.1)Liu混沌系统的电路仿真,验证了树形电路单元的有效性,证实分数阶Liu混沌系统中确实存在混沌现象,且存在混沌的最低阶数为0.3. 设计简单有效的线性反馈控制器,实现了分数阶Liu混沌系统的混沌控制. 关键词： 分数阶Liu系统 电路实验 混沌控制     

基于最小二乘支持向量机的混沌控制

利用支持向量机良好的非线性函数逼近和泛化能力，提出基于最小二乘支持向量机非线性补偿的混沌控制新方法.应用最小二乘支持向量机离线辨识混沌系统的非线性部分，并用辨识模型补偿系统的非线性，同时应用线性状态反馈控制混沌系统.对三种典型连续混沌系统的仿真研究表明，提出的控制方法可以有效的控制混沌系统到达设定的目标状态，并且由线性状态反馈控制器构成的闭环系统稳定. 关键词： 混沌控制 支持向量机 最小二乘支持向量机 状态反馈 稳定性     

Hénon混沌系统广义预测函数控制快速收敛算法

提出一种具有收敛跟踪性能的Hénon混沌系统广义预测函数控制快速算法.基于已有的广义预测函数控制方法,依据混沌系统运动特性和实际中控制量变化趋势选取特殊形式的基函数,避免了控制律中的矩阵求逆计算,并在性能指标函数中引入确定的前馈增益矩阵,实现Hénon混沌系统对参考信号的收敛跟踪.仿真结果验证了该算法的有效性. 关键词： 广义预测控制 预测函数控制 Hénon混沌系统 前馈增益矩阵     

非线性系统混沌运动的神经网络控制

设计前馈反传神经网络控制非线性系统混沌运动的新方法.根据扰动参数模型输入输出数据,按照非线性学习算法训练网络产生系统稳定所需的小扰动控制信号,去镇定混沌运动,使嵌入在混沌吸引子中的不稳定周期轨道回到稳定不动点上.Hnon映射数值仿真结果表明,这种方法控制非线性混沌系统响应速度快、控制精度高 关键词： 混沌控制 神经网络 吸引子 非线性     

混沌系统的遗传神经网络控制

提出遗传神经网络控制混沌新方法.将小扰动技术和周期控制技术结合起来，用遗传算法训练神经网络，使之成为混沌控制器.对Henon映射和Logistic映射的仿真结果说明控制器能产生小扰动控制序列信号，将混沌振荡转变成规则运动状态.该方法无需了解动态系统数学模型，具有一定抗噪声干扰能力，可将它推广应用到其他混沌系统的控制中. 关键词： 遗传算法 神经网络 混沌 周期控制