非连续的线性耦合方法实现超混沌系统的同步

基于李亚普诺夫稳定性理论, 严格证明了一类超混沌系统在间歇线性单向耦合下可以实现完全同步. 线性控制器通过一个开关函数来调节来实现‘停’和‘控’. 第一类开关函数由一个等幅度矩形波来控制, 控制器的打开和关闭选取不同的间隔周期(T_a, T_b); 第二类开关函数由一个等幅度方波来控制, 方波间隔周期记为T₀; 首先通过构造指数类型的李亚普诺夫论证了两类开关函数调制下两个超混沌 系统在单向线性耦合下实现同步的可行性问题. 为了定量分析控制效果, 定义了一定周期内控制器的平均能耗. 在数值计算中, 对第一类矩形波函数情形则计算了二参数空间(T_a, T_b)下响应系统的最大李亚普诺夫指数分布, 同步区域/非同步区域分布, 控制器平均能耗分布, 确认在恰当的间隔周期(T_a, T_b)和耦合强度下,两个超混沌系统可以达到完全同步. 对第二类方波函数情形则计算了耦合强度和方波间隔周期T₀而参 数区域内响应系统最大条件李亚普诺夫指数分布, 给定耦合强度下选择不同间隔周期下误差函数演化和平均能耗, 研究结果表明: 在恰当的耦合强度和间隔周期T₀下两个超混沌系统可以达到完全同步. 同时发现, 在恰当的耦合强度下控制器的平均能耗最小, 数值计算结果验证了理论分析的可靠性. 关键词： 超混沌 脉冲函数 指数型李函数 线性耦合     

分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

间歇同步分数阶统一混沌系统

根据分数阶微分方程的性质,研究了间歇控制分数阶系统的稳定性,提出了间歇控制分数阶系统的一般理论并给出了数学证明. 根据该理论设计控制器实现了分数阶统一混沌系统的间歇同步, 数值仿真验证了该理论的正确性. 关键词： 分数阶 统一混沌系统 间歇同步 稳定性     

基于分数阶滑模面控制的分数阶超混沌系统的投影同步

本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性. 关键词： 分数阶滑模面滑模控制器 稳定性分析 分数阶超混沌系统 投影同步     

统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步     

基于非线性控制的超混沌Chen系统混沌同步

研究了基于非线性控制的超混沌Chen系统的混沌同步问题.基于Lyapunov稳定性理论，设计了非线性控制器，改进了Jiang和Huang等设计的同步误差系统的Lyapunov函数形式，理论证明了超混沌Chen系统的自同步和超混沌Chen系统与超混沌R?ssler系统的异结构同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 超混沌Chen系统 自同步 异结构同步 非线性控制器     

参数未知的统一超混沌系统自适应反同步

文章研究了参数未知的统一超混沌系统的控制与同步问题.首先基于Lyapunov稳定性理论,设计了自适应控制器,证明了该控制器可使参数未知统一超混沌系统渐近稳定于不动点.其次使用自适应反同步方法,设计了自适应同步控制器,实现了参数未知统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 自适应反同步     

参数未知的分数阶超混沌Lorenz系统的自适应追踪控制与同步

基于分数阶系统稳定性理论,设计了控制器和未知参数的辨识规则,实现了分数阶超混沌Lorenz系统同给定信号的追踪控制与同步.数值仿真证实了所设计的控制器及未知参数辨识规则的有效性. 关键词： 分数阶 超混沌 追踪控制与同步 自适应     

随机扰动下一般混沌系统的H∞同步

本文对随机扰动下的一般混沌系统进行了H_∞控制同步研究,其中扰动是布朗运动随机过程.基于随机李雅普诺夫稳定性理论、线性矩阵不等式、It公式以及H_∞控制方法,通过设置控制器,从理论上提出了驱动系统和随机扰动下的响应系统的H_∞渐近同步的新标准,这些标准形式简单且易于用Matlab实现.最后的数值模拟表明提出的理论结果的正确性和有效性. 关键词： 随机扰动 H_∞同步')" href="#">H_∞同步 线性矩阵不等式 It公式     

一类五阶超混沌电路系统的加速追踪控制与投影同步

设计了一种统一形式的非线性状态反馈控制器,实现了一类五阶超混沌电路系统的状态变量与任意给定参考信号的追踪广义投影同步.通过取不同的比例因子和加速因子,可以快速获得与超混沌系统和多个不同维混沌系统之间的异结构广义投影同步、周期信号的广义投影同步,以及将五阶超混沌系统快速控制到周期态和期望的平衡点.数值仿真进一步表明了该方法的有效性. 关键词： 超混沌电路 追踪控制 广义投影同步 加速因子     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Robust fault-sensitive synchronization of a class of nonlinear systems

Aiming at enhancing the quality as well as the reliability of synchronization,this paper is concerned with the fault detection issue within the synchronization process for a class of nonlinear systems in the existence of external disturbances.To handle such problems,the concept of robust fault-sensitive (RFS) synchronization is proposed,and a method of determining such a kind of synchronization is developed.Under the framework of RFS synchronization,the master and the slave systems are robustly synchronized,and at the same time,sensitive to possible faults based on a mixed H /H ∞ performance.The design of desired output feedback controller is realized by solving a linear matrix inequality,and the fault sensitivity H index can be optimized via a convex optimization algorithm.A master-slave configuration composed of identical Chua’s circuits is adopted as a numerical example to demonstrate the effectiveness and applicability of the analytical results.     

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     

The H_∞ synchronization of nonlinear Bloch systems via dynamic feedback control approach

We consider an H ∞ synchronization problem in nonlinear Bloch systems.Based on Lyapunov stability theory and linear matrix inequality formulation,a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization.Moreover,this controller reduces the effect of an external disturbance to the H ∞ norm constraint.A numerical example is given to validate the proposed synchronization scheme.     

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

The recently proposed quantum control method called self‐fulfilling prophesy is investigated in multi‐level cases, based on a sequence of measurement‐feedback operations. The feedback operation is elaborately designed with respect to the eigenstates of the density matrix of the target state and its post‐measurement state. This design procedure is suitable for the generation of any predefined coherent superpositions of multiple quantum states and elicitation of desired quantum dynamics. For the sake of clearness, arbitrarily prescribed superposition states in three‐ and four‐level systems are prepared, and quantum dynamics achieved as desired. The simulation results indicate that the scheme tolerates modest imprecisions of feedback operation and is robust against sudden perturbations. Thus, the scheme enables new insight on quantum manipulations in a variety of multi‐level systems to be achieved.     

OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

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.     

间隙线性反馈控制混沌

提出了两种控制混沌的线性间隙反馈方法.该方法由控制相和非控制相组成,通过选取合适的反馈系数和控制相时间,可以获得各种不同的所需稳定的周期轨道.分别对一维的声光双稳系统和二维的类Henon吸引子进行计算机模拟,表明该方法可以使既定的系统按照给定的周期轨道演化,并且是大范围可控的. 关键词： 间隙线性反馈 混沌 类Henon映射 Lyapunov指数     

基于飞行器网络控制系统的多速率控制器设计

为了减少网络环境中的时延和数据包丢失对飞行器网络控制器系统的影响,设计了一种具有多速率的保性能控制器设计方法;多速率是指在具有多通道数据传输的系统中,各通道所需控制输入的频率不完全相同;在存在时延和丢包的情况下,利用增广技术对飞行器控制系统在整个循环周期内建立离散模型,此时为了使多速率控制方法更加有效,先基于此模型在控制器输入端构造一个预测器,根据预测器的输出为整个系统设计一个具有多控制速率的动态输出反馈控制器;然后给出并证明保性能控制器的存在条件和求解方法;最后通过某飞行器网络控制系统的数值算例验证了所提方法的有效性。     

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.