A simple asymptotic trajectory control of full states of a unified chaotic system

A simple full-state asymptotic trajectory control (FSATC) scheme is proposed to asymptotically drive full states of a unified chaotic system (UCS) to arbitrary desired trajectories. The FSATC uses only information, i.e. one state of the UCS. A sinusoidal wave and two chaotic variables are taken as illustrative tracking trajectories to verify that using the proposed FSATC can make full UCS states track desired trajectories with high tracking accuracy in a finite time.     

复杂Dynamos混沌系统的追踪控制与同步

基于系统稳定性理论,设计合适的新型非线性反馈控制器,实现复杂Dynamos混沌系统的状态向量与任意给定的不同参考信号追踪广义投影同步.以追踪控制超混沌系统、混沌系统、正弦余弦信号以及不动点为例,通过改变比例因子,可以获得多个不同混沌系统之间的异结构广义投影同步以及与正弦波形的广义同步,或者将复杂Dynamos混沌系统控制到期望的平衡点.数值仿真进一步表明了该方法的有效性. 关键词： 复杂Dynamos混沌系统 追踪控制 广义投影同步 平衡点     

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     

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.     

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.     

单向耦合网络连接的Lorenz系统的追踪控制

基于Lyapunov稳定性理论，将单个Lorenz系统的一种追踪控制方案用于单向耦合网络连接的Lorenz系统. 只对网络系统的一个节点加入控制器，就实现了单向耦合网络连接的Lorenz系统的单个输出变量对任意给定参考信号的追踪. 数值仿真表明，当网络的耦合强度足够大时，可以实现包括同结构和异结构系统信号之间的有效追踪. 关键词： Lorenz混沌系统 复杂动态网络 追踪控制 单向耦合     

不确定时变混沌系统的一种自适应无抖振变结构控制

混沌系统的一般变结构控制方法存在高频抖振和需要事先已知系统不确定项的上界等不足，针对这些不足，以一类不确定时变混沌系统为例，提出了自适应无抖振变结构控制（ACFVSC）方法，以控制混沌系统到任意设定轨道.该方法不仅能消除滑模面附近的抖振现象，实现渐近跟踪，而且不需要“不确定项的上界已知”的先验知识.ACFVSC的渐近跟踪分析与仿真结果都表明，只要选择合适的控制器参数，就能在有限时间内达到任意的设定跟踪精度. 关键词： 不确定时变混沌系统 变结构控制 无抖振     

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.     

ADAPTIVE NONLINEAR FEEDBACK CONTROL OF CHAOTIC SYSTEMS BASED ON REDUCED PARAMETER QUADRATIC PREDICTORS

An adaptive nonlinear feedback-control method is proposed to control continuous-time chaotic dynamical systems, where the adaptive nonlinear controller acts on only one-dimensional error signal between the desired state and the observed chaotic state of a system. The reduced parameter adaptive quadratic predictor used in adaptive feedback cancellation of the nonlinear terms can control the system to any desired state. Computer simulation results on the Lorenz system are shown to demonstrate the effectiveness of this feedback-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.     

Controlling chaos based on an adaptive nonlinear compensator mechanism

The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.     

混沌的可加性

从理论上推导了由几个混沌时间序列构成的新序列的动力学特性，提出了可加性的概念.计 算机仿真结果说明，新的时间序列具有分维吸引子，对初始值很敏感，两条邻近轨道随着时 间的增加呈现指数分离，具有短期可预测性，因此新序列也是混沌序列，即混沌具有可加性 .混沌时间序列的可加性理论不仅具有重要的理论意义，而且具有重要的应用价值，它是研 究多跳频电台的跳频码的理论基础. 关键词： 混沌时间序列 吸引子 分维 可加性     

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.     

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     

利用标量控制器实现一类混沌系统同步

研究了一类混沌系统的混沌同步，对此类混沌系统，通过设计一个合适标量控制器，可以实现系统的混沌同步.给出了该标量控制器设计的一般方法，并从理论上得到了混沌同步的充分和必要条件，且此充分和必要条件与混沌系统的性质无关. 关键词： 混沌系统 标量控制器 混沌同步     

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.     

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     

Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling

It is demonstrated that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, the conditions of chaos emergence are studied and the dynamics both in the regular and chaotic regimes is reported. The critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions and problem parameters, that is the SOC and/or Zeeman constants, is observed. The transition to chaotic regime is further verified by the analysis of phase portraits as well as Lyapunov exponents spectrum. The considered chaotic behavior can occur in solid state systems, weakly relativistic plasmas, and cold atomic gases with synthetic gauge fields and spin-related couplings.     

混沌系统的注入反馈控制与动态控制方法研究

提出了注入反馈控制混沌的方法,把蔡氏电路混沌系统控制到指定的平衡态和希望的振荡周期轨道上.通过改变控制参数,研究了几个典型物理状态变化现象,丰富了蔡氏电路混沌系统的应用方法 关键词： 混沌 平衡态 极限环     

New prediction of chaotic time series based on local Lyapunov exponent

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.