分数阶混沌系统滑模变结构控制

发布时间：2018-06-29 02:09

  本文选题：分数阶混沌系统 + 变结构控制　； 参考：《东北石油大学》2017年硕士论文

【摘要】：在实际工程应用与现实生活中,广泛的存在非线性现象,而在近年来,分数阶混沌系统已经成为非线性科学中的热点问题。对于分数阶混沌系统的同步控制是一种特殊的控制问题,在生物工程和信号安全等领域内具有潜在应用价值。混沌理论在许多高精尖的领域中都有运用。分数阶混沌系统同时兼具混沌系统和分数阶动力学系统的特性,这个巨大的优势使得分数阶混沌系统在混沌保密通信领域中占有一席之地。因此十分有必要对分数阶混沌动态系统的同步与控制展开理论和应用方面的研究。本文结合分数阶微积分理论,利用分数阶稳定性和Lyapunov稳定性理论与性质,对于分数阶混沌系统进行稳定性分析,控制与同步研究,主要研究内容如下:1.研究混沌系统,分数阶微积分的概念以及分数阶混沌系统的基本概念,研究滑模变结构控制的基本概念,并应用传统滑模变结构控制方法及分数阶微分方程的稳定性理论,设计滑模控制器来达成分数阶Liu系统的同步。然后进行数值模拟,证明控制器的有效性。2.在分数阶混沌系统和滑模变结构控制理论的基础上,基于终端滑模控制理论,设计了一种分数阶非奇异终端滑模面,针对系统中存在未知边界的扰动与不确定性设计了自适应控制器,使误差系统在有限时间内到达平衡点,并应用Lyapunov稳定性理论证明其稳定性。运用Matlab-simulink对于三维分数阶Chen混沌系统进行数值仿真;在不消除非线性项的情况下,设计了一种自适应滑模控制器,并证明了其稳定性。最后对于四维分数阶Lorenz系统进行数值仿真,证实了控制器的可行性。3.对分数阶混沌系统所得到的误差系统中的线性与非线性部分构建模型,对线性部分进行动态柔性变结构控制器的设计,而对于非线性部分则进行自适应滑模控制器的设计,并运用分数阶稳定性和Lyapunov稳定性理论证明控制器的稳定性。最后分别对与三维分数阶Chen系统进行仿真,证实了柔性变结构同步控制器的优势以及有效性。
[Abstract]:In practical engineering applications and in real life, there are widespread nonlinear phenomena, but in recent years, fractional chaotic systems have become a hot issue in nonlinear science. Synchronization control for fractional chaotic systems is a special control problem, which has potential application value in the fields of bioengineering and signal security. Chaos theory is applied in many sophisticated fields. Fractional chaotic systems have the characteristics of both chaotic systems and fractional order dynamical systems. This great advantage makes fractional chaotic systems have a place in the field of chaotic secure communication. Therefore, it is necessary to study the theory and application of synchronization and control of fractional chaotic dynamic systems. In this paper, the fractional order stability and Lyapunov stability theory are used to analyze, control and synchronize the fractional order chaotic system. The main contents of this paper are as follows: 1. The concepts of chaotic systems, fractional calculus and fractional chaotic systems are studied, and the basic concepts of sliding mode variable structure control are studied. The traditional sliding mode variable structure control method and the stability theory of fractional differential equations are applied. A sliding mode controller is designed to synchronize fractional-order Liu systems. Then numerical simulation is carried out to prove the effectiveness of the controller. 2. 2. Based on fractional chaotic system and sliding mode variable structure control theory, a fractional order nonsingular terminal sliding mode surface is designed based on terminal sliding mode control theory. An adaptive controller is designed for disturbances and uncertainties with unknown boundaries in order to make the error system reach the equilibrium point in a finite time. The Lyapunov stability theory is applied to prove its stability. Using Matlab-Simulink to simulate the three-dimensional fractional Chen chaotic system, an adaptive sliding mode controller is designed without eliminating the nonlinear term, and its stability is proved. Finally, the numerical simulation of the four-dimensional fractional Lorenz system proves the feasibility of the controller. The linear and nonlinear parts of the error system obtained from fractional chaotic systems are modeled, the dynamic flexible variable structure controller is designed for the linear part, and the adaptive sliding mode controller is designed for the nonlinear part. The stability of the controller is proved by the theory of fractional stability and Lyapunov stability. Finally, the simulation results with the three-dimensional fractional Chen system prove the advantages and effectiveness of the flexible variable structure synchronization controller.
【学位授予单位】：东北石油大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;TP273
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本文编号：2080359