具有切换输出的分数阶切换混沌系统同步及其在保密通讯中的应用

Based on the new output model: the switched output which is proposed by us, this subject mainly discusses the chaos synchronization of fractional-order switched chaotic systems with switched output and its application in secure communication. We suppose that the drive system is a switched system which can be switched between different systems. The output of the drive system is assumed to be switched between different outputs. This subject intends to consider several interesting chaos synchronization problems (Please see the research contents and the research aim section in the body). For each problem, the sufficient conditions for chaos synchronization are presented via proper controller which is designed by only using the switched output. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control approach. By selecting the appropriate switching parameters the synchronization of fractional-order switched chaotic system with switched output can be reduced to the classical synchronization which means that it is a generalization of the classical synchronization. Since a single chaos system only meets a dynamic equation while the switched system can satisfy two or more dynamic equations simultaneously, thus the dynamic characteristics of switched chaotic system is more complex than that of a single chaotic system which means that the switched chaotic system has better pseudo randomness than that of a single chaotic system. On the other hand, because of the complexity of the continuous output is higher than that in switched output, thus the signal transmitted by our model maybe have stronger anti-attack ability and anti-translated capability than that transmitted by the usual model. Therefore, the studies of this project will not only enrich the synchronization theory of chaotic systems but also have important practical significance.

基于作者提出的新输出模式：切换输出，本课题讨论含有切换输出量的分数阶切换混沌系统同步及其在保密通讯中的应用。假定驱动系统是切换系统，它可以在多个结构完全不同的系统之间进行切换且其输出量也可在不同输出量之间进行切换。通过用切换输出量来设计控制器本课题考虑几个感兴趣的同步问题，对每个问题给出同步的充分条件并用数值模拟验证所给方法的有效性。经过选择适当的切换参数可把含有切换输出量的切换混沌系统同步化为经典的同步方式，因而它是经典同步的推广。由于单一的混沌系统只满足一个动力学方程，而切换系统则同时满足2个或2个以上的动力学方程，因此切换混沌系统具有比单一混沌系统更复杂的动力学特性和更好的伪随机性。同时由于切换输出比连续输出具有更高的复杂性，因而由含有切换输出量的切换混沌系统传输信号比由传统方式传输的信号具有更强的抗干扰性及更高抗破译性。因此本课题的研究不仅会丰富混沌同步理论知识且具重要的现实意义。

混沌理论由于其在保密通信、系统控制、生物、物理、化学等领域具有潜在的应用价值而得到了广泛的研究。 基于作者提出的新输出模式：切换输出，本课题主要讨论含有切换输出量的分数阶切换混沌系统同步及其在保密通讯中的应用。根据项目申请书，我们把本项目的主要研究内容及重要结果概括为以下5个方面：. (1) 讨论了分数阶混沌系统的控制与同步。不仅考虑了单输出分数阶系统、脉冲分数阶系统的控制与同步，同时利用加幂积分器法考虑了具有外部扰动的三维不确定分数阶混沌系统的鲁棒控制与同步。由于现实生活中的系统其状态变量不一定是完全可以获得的，有可能只有某一个状态变量是可得的，也有可能只能够间断获得，因此考虑单输出分数阶系统、脉冲分数阶系统的控制与同步具有重要的理论与实际意义。. (2) 提出了一种实现混沌系统控制与同步的新方法—精确解法，通过构造系统的精确解不仅考虑了3维混沌系统的控制与同步而且还考虑了n维混沌系统的控制与同步。精确解法其优点有以下方面：其一是知道系统的精确解；其二是比较容易构造李雅普诺夫函数；其三是可以知道系统的收敛速率。. (3) 利用滑模控制、自适应控制、饱和控制等考虑了混沌系统(混沌神经网络)的固定时间控制与同步，得到一系列的固定时间稳定定理。这些固定时间稳定定理不仅是我们所发的文章的理论基础，也为其他研究固定时间控制与同步的学者提供理论支撑。. (4) 基于扭转控制器(the twisting controller)考虑了一类混沌系统的有限时间控制与同步。. (5) 通过构造观测器考虑了单输出混沌系统的同步与参数估计。