Mathematics and Computers in Simulation ( IF 4.6 ) Pub Date : 2020-12-29 , DOI: 10.1016/j.matcom.2020.12.022 Hamid Hamiche , Hocine Takhi , Manal Messadi , Karim Kemih , Ouerdia Megherbi , Maamar Bettayeb
This paper presents new synchronization results for a class of nonlinear discrete-time chaotic systems based on a synergetic observer design with a circuit implementation. The synchronization master–slave method adopted is based on the synergetic theory which is exploited to propose a synergetic observer. The system (master) adopted is that of the discrete-time Lur’e forms. One of the main contributions of this paper is to exploit this simple special form as master in order to design a synergetic observer (slave) which allows us to control the rate of convergence of the synchronization error using the synergetic design parameter matrix. In order to achieve the synchronization method, sufficient conditions for asymptotic synchronization are given. Two simulation examples are provided to show the effectiveness of the method in two different cases: the master system respects and does not respect the Lur’e form. Furthermore, experimental implementation results using Arduino boards are illustrated to validate the proposed approach.
中文翻译:
基于协同观测器的一类非线性离散时间混沌系统的新同步结果及其实现
本文提出了基于协同观测器设计和电路实现的一类非线性离散时间混沌系统的新同步结果。所采用的同步主从方法基于协同理论,该理论被用来提出协同观测器。采用的系统(主系统)是离散时间Lur'e形式的系统。本文的主要贡献之一是利用这种简单的特殊形式作为母版,以设计一个协同观测器(从机),该协同观测器使我们能够使用协同设计参数矩阵来控制同步误差的收敛速度。为了实现同步方法,给出了渐近同步的充分条件。提供了两个仿真示例,以显示该方法在两种不同情况下的有效性:主系统尊重并且不尊重Lur'e形式。此外,还说明了使用Arduino开发板的实验实现结果,以验证所提出的方法。