分数阶混沌系统的控制与同步研究

发布时间：2018-08-04 13:47

【摘要】：分数阶微积分理论可以追溯到十七世纪,由于其在科学与技术领域的广泛应用,使得分数阶微积分在二十世纪得到了全面的发展。另一方面,混沌作为非线性动力学系统的一种特有运动形式,在物理、金融以及生命科学等众多领域受到了广泛的关注和研究。由于分数阶混沌的动力学行为和系统阶次紧密关联且具有一定的历史记忆特性,所以动力学特性往往比整数阶混沌系统更为复杂,在图像处理和保密通信等领域的应用前景非常广阔。近年来,随着计算机技术的迅猛发展,越来越多的研究者针对分数阶混沌系统的控制与同步问题展开了研究,但由于相关研究起步较晚,所以相关理论体系和技术还亟需进一步的完善。因此,本论文将在前人工作的基础上,进一步研究分数阶混沌系统的控制、同步及其应用问题。具体内容和已取得的研究结果简要叙述如下:首先,针对分数阶混沌系统的控制问题,提出了两种不同的控制策略。一种是针对分数阶统一混沌系统,研究了非脆弱模糊控制;另一种是针对一类分数阶非线性系统,研究了有限时间镇定问题。数值仿真验证了所提方法对于解决分数阶混沌系统镇定问题的有效性。其次,针对分数阶混沌系统的同步问题,提出了两种不同的同步策略。一种是针对三个结构相同阶次相同的分数阶混沌和超混沌系统,研究了模糊自适应函数组合投影同步问题;另一种是针对两个异结构异阶次分数阶混沌系统,研究了基于主动控制的自适应投影同步问题。数值仿真验证了所提方法的有效性。最后,基于所提出的同步策略,设计了一种基于异结构异阶次分数阶混沌系统同步的混沌保密通信方案。该方案不仅能够有效的实现信息传输而且进一步提高了通信的安全性。利用正弦函数和方波信号作为有用信号对基于分数阶混沌同步的保密通信方案进行了仿真验证,结果表明了所提保密通信方案的有效性。
[Abstract]:Fractional calculus can be traced back to the seventeenth Century. Because of its extensive application in the field of science and technology, fractional calculus has been developed in a comprehensive way in twentieth Century. On the other hand, chaos is a unique form of motion of nonlinear dynamic systems, in many fields, such as physics, finance and life science. The dynamic behavior of fractional order chaos is more complex than integer order chaotic system because of the dynamic behavior of fractional chaos and the order of system order. So the application prospect in image processing and secure communication is very broad. In recent years, with the rapid development of computer technology More and more researchers have studied the control and synchronization of fractional chaotic systems, but because of the late start of the related research, the relevant theoretical system and technology need to be further improved. Therefore, this paper will further study the control, synchronization and synchronization of fractional chaotic systems on the basis of previous work. The specific content and the results obtained are briefly described as follows: firstly, two different control strategies are proposed for the control problem of fractional order chaotic systems. One is to study the non fragile fuzzy control for a fractional order unified chaotic system, and the other is for a class of fractional nonlinear systems. Time stabilization problem. Numerical simulation shows the effectiveness of the proposed method for solving the stabilization problem of fractional order chaotic systems. Secondly, two different synchronization strategies are proposed for the synchronization of fractional order chaotic systems. One is a fractional order chaos and hyperchaotic system with the same order of the same order of three structures, and the fuzzy self is studied. The adaptive projection synchronization problem is adapted to the combination of functions. The other is an adaptive projection synchronization problem based on active control for two different order fractional order chaotic systems. Numerical simulation shows the effectiveness of the proposed method. Finally, based on the proposed synchronization strategy, a kind of different order fractional order chaos is set up. The system synchronization chaotic secure communication scheme. This scheme not only can effectively carry out information transmission but further improve the security of communication. Using sinusoidal and square wave signals as useful signals, the simulation verification of secure communication scheme based on fractional chaotic synchronization is carried out. The results show that the proposed secure communication scheme is proposed. Validity.
【学位授予单位】：河南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;O231

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