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     

Tracking control and synchronization of chaotic systems based upon sampled—data feedback

A novel tracking control and synchronization method is proposed based upon sampled-data feedback.This method can make a chaotic system approach any desired smooth orbit and synchronize the driving system and the response system,both in the same structure and in diverse structures.Finally,a numerical simulation with a Lorenz system is provided for the purpose of illustration and verification.     

基于引力场理论的混沌同步

通过引入分布引力场,将混沌系统的同步问题等效为引力场中系统运行轨道一致问题,从而实现更多不同动力学混沌系统的同步.通过将混沌系统之间的耦合度定义为速度,因其与运动方程无关,从而有别于常见的混沌同步控制项,具有较强通用性.基于轨道逼近导出引力场中多个混沌系统同步的条件,给出同步轨道方程.数值仿真实验说明了该方法的有效性.     

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     

Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network

Aiming at regional services,the space segment of COMPASS (Phase I) satellite navigation system is a constellation of Geostationary Earth Orbit (GEO),Inclined Geostationary Earth Orbit (IGSO) and Medium Earth Orbit (MEO) satellites.Precise orbit determination (POD) for the satellites is limited by the geographic distribution of regional tracking stations.Independent time synchronization (TS) system is developed to supplement the regional tracking network,and satellite clock errors and orbit data may be obtai...     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

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。     

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.     

Intermittent lag synchronization in a driven system of coupled oscillators

We study intermittent lag synchronization in a system of two identical mutually coupled Duffing oscillators with parametric modulation in one of them. This phenomenon in a periodically forced system can be seen as intermittent jump from phase to lag synchronization, during which the chaotic trajectory visits a periodic orbit closely. We demonstrate different types of intermittent lag synchronizations, that occur in the vicinity of saddle-node bifurcations where the system changes its dynamical state, and characterize the simplest case of period-one intermittent lag synchronization.     

基于模糊滑模的有限时间混沌同步实现

提出了混沌同步有限时间实现问题.应用全程滑模控制技术，选择指数型终端滑模趋近律来设计滑模控制器，以实现一类混沌系统的状态同步.该设计方案针对混沌系统的参数不确定性和外界扰动，引入模糊基函数网络，在线估计不确定性和外部扰动的界值.同时该方案消除了滑模控制的到达阶段，状态始终保持在滑模面上，并能在有限时间内趋近于原点.最后以Duffing系统为例研究验证同步策略的可行性和有效性.     

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.     

Satellite-station time synchronization information based real-time orbit error monitoring and correction of navigation satellite in Beidou System

Satellite-station two-way time comparison is a typical design in Beidou System(BDS)which is significantly different from other satellite navigation systems.As a type of two-way time comparison method,BDS time synchronization is hardly influenced by satellite orbit error,atmosphere delay,tracking station coordinate error and measurement model error.Meanwhile,single-way time comparison can be realized through the method of Multi-satellite Precision Orbit Determination(MPOD)with pseudo-range and carrier phase of monitor receiver.It is proved in the constellation of 3GEO/2IGSO that the radial orbit error can be reflected in the difference between two-way time comparison and single-way time comparison,and that may lead to a substitute for orbit evaluation by SLR.In this article,the relation between orbit error and difference of two-way and single-way time comparison is illustrated based on the whole constellation of BDS.Considering the all-weather and real-time operation mode of two-way time comparison,the orbit error could be quantifiably monitored in a real-time mode through comparing two-way and single-way time synchronization.In addition,the orbit error can be predicted and corrected in a short time based on its periodic characteristic.It is described in the experiments of GEO and IGSO that the prediction accuracy of space signal can be obviously improved when the prediction orbit error is sent to the users through navigation message,and then the UERE including terminal error can be reduced from 0.1 m to 0.4 m while the average accuracy can be improved more than 27%.Though it is still hard to make accuracy improvement for Precision Orbit Determination(POD)and orbit prediction because of the confined tracking net and the difficulties in dynamic model optimization,in this paper,a practical method for orbit accuracy improvement is proposed based on two-way time comparison which can result in the reflection of orbit error.     

Chen系统的自适应追踪控制

利用非线性单输入控制器实现混沌Chen系统的自适应追踪控制.根据Chen系统的结构特点选取合适的反馈方式，设计单输入自适应控制器，使Chen系统自适应追踪参数未知的Rossler系统的某一变量，并由Lyapunov直接方法证明误差信号渐近稳定于零.数值仿真结果表明该控制方法可行，且可以实现未知参数的辨识.     

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.     

Hénon混沌系统的追踪控制与同步

基于离散线性系统的稳定性理论,实现了Hénon混沌系统对参考信号的追踪控制.讨论了系统的同步问题,给出了“异结构混沌同步”的新概念.数值仿真表明了本文方法的有效性 关键词： Hénon混沌系统 追踪控制 混沌同步     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

GLOBAL CHAOS CONTROL OF NON-AUTONOMOUS SYSTEMS

This study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers. With Euler's method, a non-autonomous system is approximated by a non-linear difference system and then an approximate global Poincaré map function is derived from the difference system by iterating one or more periods of a periodic excitation. Based on the map function, unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed. The global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit. Furthermore, a Lyapunov's direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. For practical applications, system models are usually unknown. To obtain a mathematical model, non-linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit.     

基于函数矩阵的一类混沌系统同步

研究了一类混沌系统的同步问题、基于稳定性理论和极点配置技术,设计了两个混沌系统之间的同步方案,实现两个混沌系统之间的同步,通过函数矩阵,实现驱动系统和响应系统的状态变量按给定的函数矩阵同步,同时证明了该方法同样适用于两个混沌系统之间的滞后同步,通过对Lorenz混沌系统和Lorenz超混沌系统的数值模拟,进一步验证了所提方案的有效性。     

Hénon混沌系统的广义预测控制与同步快速算法

提出了一种带有终端滑模等式约束的Hénon混沌系统的广义预测控制快速算法.该方法将广义预测控制与离散滑模控制结合起来运用到Hénon混沌系统中，并采用柔化输入信号的方法，避免了广义预测控制算法中的高维矩阵求逆.占用内存小，计算速度快，并且具有较强的跟踪给定信号和抑制系统参数摄动和随机噪声的能力.仿真结果验证了该方法的有效性和快速性. 关键词： 广义预测控制 离散滑模控制 Hénon混沌系统 混沌同步