递增二次约束混沌系统基于圆判据观测器的同步  

Incremental Quadratic-Constrained Chaotic System based on Synchronization of Circular-Criterion Observer

作　　者：赵友男 章伟[1,2] 宋芳[1] ZHAO You-nan;ZHANG Wei;SONG Fang(Laboratory of Intelligent Control and Robotics,Shanghai University of Engineering Science,Shanghai 201620,China;MOE Key Laboratory of Image Processing and Intelligence Control,Huazhong University of Science and Technology,Wuhan Hubei 430074,China)

机构地区：[1]上海工程技术大学智能控制和机器人实验室,上海201620 [2]华中科技大学教育部图像处理与智能控制重点实验室,湖北武汉430074

出　　处：《通信技术》2018年第11期2709-2714,共6页Communications Technology

基　　金：国家自然科学基金(No.51505273;No.61603241);图像信息处理与智能控制教育部重点实验室开放基金(No.IPIC2015-02)~~

摘　　要：递增二次约束包含了经典的Lipschitz条件、递增扇形有界条件以及单边Lipschitz条件等许多非线性约束条件。该约束条件主要由递增乘数矩阵来描述,一定程度上为常见的非线性提供了一种统一描述。因此,选取一类满足递增二次约束的混沌系统作为研究对象,设计了基于圆判据观测器的混沌同步方案。该方案为大多数常见的混沌系统提供了一种通用的基于观测器的同步方法。观测器系统的估计误差以指数速率收敛到0,实时性较好,而观测器存在的充分条件通过线性矩阵不等式的形式给出,易于求解。最后,以统一混沌系统为例,通过数值仿真说明了该同步方案的有效性。The incremental quadratic constraint is a special case of many nonlinear constraints including classical Lipschitz conditions, incremental fan bounded conditions, and one-sided Lipschitz conditions. This constraint is primarily described by an incremental multiplier matrix. To a certain extent, this condition provides a uniform description for common nonlinearities. In order to satisfy the chaotic system with increasing quadratic constraints, a chaotic synchronization scheme based on the circular criterion observer is designed. This scheme provides a common observer-based synchronization method for most common chaotic systems. The estimation error of the observer system converges to zero at an exponential rate, with fairly good real-time performance. At the same time, the sufficient conditions for the existence of observer are given in the form of linear matrix inequalities, which are easy to solve. Finally, by taking the unified chaotic system as an example, the numerical simulation results indicate the effectiveness of this synchronization scheme.

关 键 词：递增二次约束条件 线性矩阵不等式 圆判据观测器 混沌同步 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]