混沌与分数阶混沌系统同步控制研究及其电路仿真

混沌与分数阶混沌系统同步控制研究及其电路仿真文章来源：伟智论文服务中心 [打印]【摘要】混沌作为一种复杂的非线性运动行为,在物理学、化学、信息技术以及工程学等领域得到了广泛的研究。

由于混沌对初值的极端敏感性、内在的随机性、连续宽谱等特点,使其特别适用于保密通信、信号处理、图象加密等领域,因此,混沌同步成为混沌应用的关键技术。

在参阅大量文献的基础上,本文利用理论证明,数值模拟以及电路仿真相结合的方法,对混沌系统同步、分数阶超混沌系统同步、以及非自治超混沌系统进行了研究。

本文的主要研究内容如下:1.基于Lyapunov稳定性理论,利用自适应控制方法,以不确定单模激光Lorenz系统作为驱动系统,将不确定单涡旋混沌系统作为响应系统,设计了非线性反馈控制器及参数识别器,使响应系统的所有状态变量严格地按函数比例跟踪驱动系统的混沌轨迹,并辨识出包括非线性项在内的驱动系统和响应系统的不确定参数,利用四阶龙格库塔仿真模拟,结果表明了该方法的有效性。

2.应用驱动-响应方法、反馈线性化方法以及基于Lyapunov方程的Backstepping 控制方法,研究了分数阶超混沌L(u|¨)系统同步问题。

其次,针对上述分数阶混沌系统同步方法中存在的不足,基于分数阶系统的稳定性理论,提出了分数阶超混沌系...更多统的自适应同步方法,用两个控制器与两个驱动变量实现了不确定分数阶超混沌L(u|¨)系统的自适应同步,给出了自适应同步控制器和参数自适应率,辨识出系统的不确定参数。

最后,结合Active控制技术,实现了异结构分数阶超混沌系统的同步。

理论证明、数值模拟以及电路仿真证实了上述同步方法的有效性和可行性。

3.采用调节连续信号频率的方法,将外界控制信号引入到超混沌系统中,设计了一个新四维非自治超混沌系统。

通过精确地调节模拟输入信号的频率,观察和验证新系统的非线性动力学特性,具体为周期轨、二维环面、混沌和超混沌现象。

通过Lyapunov指数图,分岔图来解释系统的动力学特性,并且给出了设计的实验电路及其观测的结果,进一步从物理实现上验证仿真结果的准确性。

最后利用单变量耦合反馈控制方法,通过电路实验实现了非自治超混沌系统的同步。

还原【Abstract】 Chaotic systems are well known for their complex nonlinear systems, and have been intensively studied in various fields such as physics, chemistry, information technology and engineering. In virtue of its characteristics of chaos such as hyper sensitivity to initial conditions, high randomicity and board spectra for its Fourier transform, chaos can be especially applied to secure communications, signal processing and image encryption and so on. Thus chaos synchronization has become the key process in the application of chaos. The research has studied the relative problems of chaos synchronization, synchronization of fractional-order hyper-chaotic systems and analysis of a new four-dimensional non-autonomous hyper-chaotic system, usingthe methods of theoretical derivation, numerical simulation and circuitry experimental verification. The main contributions of this paper are list as follows:1. Based on Lyapunov stability theory, the nonlinear feedback controller and parameter recognizer...更多 were designed with the adaptive control method. The uncertain single-mode laser Lorenz system is taken as the drive system and the uncertain single scroll attractor chaotic system as the response system in the design, which makes all the status variable of the response system to follow the chaotic path of the drive system strictly in function proportion, and recognizes all the uncertain parameters including unknown coefficients of nonlinear terms of the drive and response systems. The result obtained by the four-order Runge-Kutta simulation indicates the effectiveness and feasibility of the method.2. Three different synchronization schemes based on the Pecora-Carroll principle, the linearization by feedback and back-stepping approach based on Lyapunov equation are proposed to realize chaotic synchronization. Some methods such as linearization feedback control method eliminate nonlinear terms of systems when designing controllers, which make the coefficient matrix of the system to be the constant matrix. Although these schemes can control the fractional-order chaotic system to synchronize, it costs too much. And then, based on fractional stability theory, the adaptive control method proposed in this paper can achieve synchronization of fractional-order hyper-chaotic systems only using two controllers, and adaptive controller and updating law of parameter are obtained. Numerical simulations confirm the effectiveness of the proposed synchronization approaches. Especially, the circuit experiment simulations also demonstrate that the experimental results are in agreement with numerical simulations. Moreover, the active control technique is applied to synchronize the different fractional-order hyper-chaotic systems, numerical simulations have performed the effectiveness and feasibility of the presented synchronization techniques.3. A new four-dimensional non-autonomous hyper-chaotic system is presented by adding input sine signal to a hyper-chaotic system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyper-chaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the non-autonomous system are analyzed. Also, the synchronizing circuits of the non-autonomous hyper-chaotic system are designed via the synchronization control method of single variable couplingfeedback. The electronic circuits are implemented and the experimental results observed by the oscillograph well agreed with the simulation results. 还原【关键词】混沌; 分数阶超混沌系统; 非自治系统; 同步控制; 自适应; 电路仿真【Key words】 chaos; fractional-order hyper-chaotic system;non-autonomous system; synchronization control; adaptive control; circuit simulation。