不确定混沌系统的反同步与参数辨识

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.     

具有非线性控制的Chua电路的混沌同步

Chua电路是一个非光滑系统.本文通过广义哈密顿系统和观测器方法,将具有非线性控制的Chua电路的混沌同步问题转化成研究具有非线性控制的光滑系统的零解稳定性;进而利用滑模控制对该光滑系统的零解稳定性进行了研究,从而使得Chua电路达到了混沌同步.最后,将上述方法应用到具体系统,数值结果也表明其正确性.     

混沌系统的变结构同步控制

研究Lorenz混沌系统的同步控制问题,提出1种在多输入的情况下实现混沌同步的变结构控制算法.利用该算法设计的变结构同步控制律使得同步误差系统的运动在切换面上成为渐近稳定的滑动模态,从而较快的实现了混沌同步.通过对 Lorenz 混沌系统的理论分析和数值仿真,说明了该变结构同步控制策略的实用性和有效性.     

基于线性反馈控制的一类混沌系统的同步

研究一类混沌系统的同步问题。基于李雅普诺夫稳定性理论,利用线性反馈法给出了同步混沌系统的3种控制方案,得到了2个混沌系统同步的充分条件。为了更清楚地了解每种方案下系统的同步行为,还给出了以增益为分岔参数时同步误差的变化图。理论分析和数值仿真结果都表明了文中所给方法的有效性和可行性。     

基于滑模方法的不确定分数阶广义系统的鲁棒无源控制

本文研究了基于滑模控制的一类不确定分数阶广义系统的可容许性和鲁棒无源性问题。首先,设计了一种含有奇异矩阵的分数阶积分型切换函数,对其求分数阶导数推导出等效控制,进而得到滑动模态方程。其次,针对滑动模态方程和系统输出方程,利用线性矩阵不等式技巧,给出了系统滑动模态具有鲁棒无源性和可容许性的充分性判据,并进一步建立了鲁棒无源可容许的可解性条件。同时,设计的分数阶滑模控制律保证了闭环系统状态轨迹能够到达预设的切换面。最后,通过一个仿真实例验证了本文结果的有效性。     

时间分数阶色散方程的高阶差分方法

时间分数阶色散方程用以描述带有记忆性的色散现象。本文研究分数阶色散方程的高精度差分方法,利用紧致差分格式的构造技巧,得到了求解时间分数阶色散方程的四点四阶和五点六阶2个紧致隐式差分格式,收敛阶分别为O(τ2+h4)和O(τ2+h6).数值算例表明本文方法是高精度有效的,且具有很好的数值稳定性。     

分数阶参数不确定系统的异结构混沌同步

利用滑模控制方法研究了一类分数阶参数不确定混沌系统的自适应同步控制问题,基于Lyapunov稳定性理论和分数阶微积分的相关理论,给出分数阶参数不确定系统取得滑模同步的充分性条件,并给出了严格的证明,研究表明,一定条件下分数阶不确定系统是滑模混沌同步的,仿真结果表明了方法的可行性。     

标量控制下的二次自治混沌系统不确定参数估计和自适应反同步

基于Lyapunov稳定性理论,设计了一个简单的标量自适应控制器分别使具有确定和不确定参数的三维(3D)二次自治混沌系统实现反同步.此外,从驱动和响应系统间的时序列动态估计出所有不确定参数. 数值仿真表明该方法的有效性和实用性.     

大规模富社团网络的时空混沌同步

以Plankton时空混沌系统作为网络节点,通过非线性耦合构成富社团(rich-club,RC)网络,研究其时空混沌同步规律.首先给出了RC网络中连接节点之间的非线性耦合函数的一般性选取原则.进而基于Lyapunov稳定性定理,理论分析了实现网络同步的条件.最后,通过仿真模拟检验了网络的时空混沌同步效果.仿真研究表明,RC网络中各富节点之间以及这些富节点各自星形连接的子网络中的所有节点均实现了完全同步.     

最近邻耦合网络的时空混沌同步研究

本文进行了最近邻网络的时空混沌同步研究.以时空混沌系统作为网络的节点,基于Lyapunov稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络完全同步的条件.采用Fisher-Kolmogorov时空混沌系统作为网络节点实例进行了仿真模拟,获得了理想的同步效果.进一步研究了有界噪声影响下网络的同步性能,结果显示它具有较强的抗干扰能力.     

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.     

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.     

An improved impulsive control approach to robust lag synchronization between two different chaotic systems

In this paper, a novel robust impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the theory of impulsive functional differential equations and a new differential inequality, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined region. Finally, some numerical simulations for the Lorenz system and Chen system are given to demonstrate the effectiveness and feasibility of the proposed method. Compared with the existing results based on so-called dual-stage impulsive control, the derived results reduce the complexity of impulsive controller, moreover, a larger stable region can be obtained under the same parameters, which can be shown in the numerical simulations finally.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

Chaos and chaotic control in a relative rotation nonlinear dynamical system under parametric excitation

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.     

(2+1)维 Korteweg-de Vries 方程的传播孤子及混沌行为

利用一个投射方程和变量分离法,得到了(2+1)维 Korteweg-de Vries (KdV) 方程的新显式精确解.根据得到的孤立波解,构造出 KdV 方程的传播孤子结构. 利用一个新的混沌系统研究了孤子的混沌行为.     

无人机海上溢油跟踪监测系统设计及仿真

海上环境变化多端,造成溢油的漂移和扩散会出现不可预测的情况,精确、实时地监测海上溢油是现今亟待解决的问题.无人机以其部署快、成本低、环境适应性强的优势在海上溢油监测领域得到重视,但单架无人机监测能力弱,而多架无人机监测的准确性仍需提高.为此,本文提出一种无人机群海面溢油自动导航跟踪监测的架构和方法,根据海上溢油浓度的变...     

动态测量系统中时间同步问题研究与实践

多传感器动态测量系统中时间严格同步是实现系统实时、准确获取空间目标位置、姿态等信息的关键。围绕解决传感器间数据同步问题,提出针对两台计算机的时间同步方案,制定传感器数据采集方案,提出相应的数据内插算法。综合测试结果表明,提出的方案及算法成功地解决了多传感器动态测量系统中的时间同步问题,系统综合测试精度优于0．05mm,远远高于0．465mm的设计指标。