基于有限时间观测器的离散系统混沌同步

本文基于驱动–响应模型针对一类离散时间混沌系统提出了一种基于有限时间观测器的同步方法. 首先, 将混沌系统写成具有未知输入的线性系统形式. 随后, 给出了观测器匹配条件和强可观条件. 在观测器匹配条件的 假设下, 通过适当的状态变换, 给出了具有降维形式的有限时间观测器设计框架使得该观测器不再受到未知输入的 影响. 然后, 证明了强可观条件结合观测器匹配条件可以保证一个有限时间观测器的存在, 该观测器可以使得响应 系统达到对驱动系统的精确同步, 且达到同步所需要的时间可以任意设定, 不受观测器系统矩阵极点配置和初值条 件的影响. 最后, 给出了两个混沌系统的例子验证了所提方法的有效性.

Finite time observer-based synchronization for discrete-time chaotic systems

Based on the drive-response configuration, this paper discusses the synchronization of a class of discretetime chaotic systems based on a finite-time observer. First, the chaotic system is written in the form of a linear system with unknown input. Subsequently, the strong observable condition and the observer matching condition are given. Under the assumption of the observer matching condition, the finite-time observer design framework with a reduced-order is given by using appropriate state transformations, where the observer is no longer affected by the unknown input. Then, the strong observable condition together with the observer matching condition guarantees the existence of a finite-time observer, which can achieve a precise synchronization between the response system and the driving system, and the synchronization time can be arbitrarily pre-defined, which neither depend on the observer gain matrix nor depend on the initial value condition. Finally, two chaotic systems are given as examples to illustrate the effectiveness of the proposed method.