分数阶忆阻混沌电路动力学分析及其滑模控制研究

发布时间：2018-01-24 22:09

本文关键词： 忆阻器分数阶系统稳定性分析混沌现象水印加密滑模控制　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：混沌学涉及自然科学与社会科学等众多领域,它是当今世界科学研究的前沿,而混沌电路的动力学以及其应用可以说是混沌学的核心问题。忆阻器作为一种全新的非线性电路元器件,它的非易失性和记忆性在混沌电路、混沌加密等方向有着巨大的应用前景。随着忆阻器的提出,忆阻混沌电路受到了国内外广泛的关注,借助简单的忆阻电路的建模分析可以有效地描述混沌电路的基本特性。近年来有研究表明分数阶微积分相比于传统整数阶微积分更能精确地描述一些特定的物理现象,所以本文将分数阶理论应用在忆阻混沌系统中,实验结果证实在分数阶忆阻电路中存在混沌现象,并且这一混沌现象能够被充分利用也能够被有效的控制。本文以忆阻混沌系统的复杂动力学现象为研究背景,从整数阶忆阻系统入手,在整数阶混沌系统的基础上推导出其分数阶形式,并对其动力学进行了深入的研究。同时,将混沌现象运用在水印加密算法中,从而有效地提高了算法的保密性。最后为了抑制混沌行为的发生,提出了分数阶滑模控制器。全文主要的创新点如下:(1)以简单的整数阶忆阻器混沌电路模型为研究起点,建立了分数阶忆阻器混沌电路的动力学模型,并利用李雅普诺夫间接法对其稳定性进行了分析。同时关注系统的非线性动力学现象,通过分岔图以及李雅普诺夫指数研究了该模型在不同参数发生变化时所存在的混沌现象。(2)以混沌系统对初始值的敏感性及其具备的混沌性为研究背景,提出了采用分数阶忆阻混沌系统对数字图像进行水印加密,并通过离散小波变换对密文水印进行嵌入以及提取。为了证明该算法的有效性,对算法的抗攻击性和对密钥的敏感性进行了详细的分析。实验结果表明基于分数阶忆阻混沌系统的水印加密算法具有较高的安全性,与其他算法相比具有更强的不可见性。(3)以分数阶忆阻混沌系统为研究对象,为了达到抑制混沌现象的目的,设计了一个分数阶滑模控制器。在确保滑模行为发生的前提下,根据Lyapunov稳定性定理以及滑模理论,选择积分型的滑模面,建立了函数切换控制方法下的滑模控制器,并推导出滑模控制器参数所要满足的条件。最后实验结果分析了控制器在不同参数下受控系统的稳定性,并给出对应的时域波形图,验证了理论分析的正确性。
[Abstract]:Chaos, which involves many fields such as natural science and social science, is the frontier of scientific research in the world today. The dynamics and application of chaotic circuits are the core problems of chaos. As a new kind of nonlinear circuit components, the non-volatile and memory properties of amnesia are in chaotic circuits. Chaotic encryption and other directions have great application prospects. With the introduction of amnesizer, the circuit of amnesia has received extensive attention at home and abroad. The basic characteristics of chaotic circuits can be described effectively by modeling and analysis of simple memory circuits. Recent studies have shown that fractional calculus can describe some specific physics more accurately than traditional integral calculus. Phenomenon. In this paper, the fractional order theory is applied to the amnesia chaotic system, and the experimental results confirm the existence of chaos in the fractional order circuit. And this chaotic phenomenon can be fully utilized or effectively controlled. In this paper, the complex dynamic phenomenon of the amnesia chaotic system is studied in the context of integer order amnesia system. Based on the integral order chaotic system, the fractional order form is deduced, and its dynamics is deeply studied. At the same time, the chaos phenomenon is applied to the watermark encryption algorithm. Thus, the secrecy of the algorithm is improved effectively. Finally, in order to suppress the occurrence of chaotic behavior. A fractional sliding mode controller is proposed. The main innovations of this paper are as follows: 1) based on the simple chaotic circuit model of integer order amnesia, the dynamic model of fractional order damper chaotic circuit is established. The stability of the system is analyzed by Lyapunov indirect method, and the nonlinear dynamics of the system is concerned. By using bifurcation diagram and Lyapunov exponent, the chaotic phenomena existing in the model with different parameters are studied.) based on the sensitivity of chaotic systems to initial values and their chaotic properties. A fractional order mnemonic chaotic system is proposed to encrypt the digital image and to embed and extract the ciphertext watermark by discrete wavelet transform to prove the effectiveness of the algorithm. The robustness of the algorithm and the sensitivity to the key are analyzed in detail. The experimental results show that the watermark encryption algorithm based on fractional order amnesia chaotic system has high security. Compared with other algorithms, it has stronger invisibility. 3) taking fractional order amnesia chaotic system as the research object, in order to achieve the purpose of suppressing chaos phenomenon. A fractional sliding mode controller is designed. Based on the Lyapunov stability theorem and sliding mode theory, the integral sliding mode surface is selected. The sliding mode controller under the function switching control method is established, and the conditions of the sliding mode controller parameters are deduced. Finally, the stability of the controlled system under different parameters is analyzed by the experimental results. The corresponding time domain waveform diagram is given to verify the correctness of the theoretical analysis.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN60

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