广义Lorenz系统的模糊建模和同步  

Fuzzy Modeling and Synchronization of Generalized Lorenz System

作　　者：单梁[1] 李军[1] 王执铨[1] 

机构地区：[1]南京理工大学自动化学院,江苏南京210094

出　　处：《控制工程》2007年第2期174-177,181,共5页Control Engineering of China

基　　金：江苏省自然科学基金资助项目(BK2004132);江苏省科技厅青年创新基金资助项目(BK2004421)

摘　　要：广义Lorenz系统包括经典Lorenz系统和无穷多个结构相似但不拓扑等价的混沌系统。针对广义Lorenz规范式(GLCF)结构,基于T-S模型进行了系统的模糊重构;利用Lyapunov稳定性理论和反馈同步的思想实现了重构系统的同步,并推导了误差系统以衰减率α实现全局渐近稳定的充分条件。统一混沌系统和扩展Liu系统均属于典型的广义Lorenz系统。利用LMI方法对这两个混沌系统所进行的仿真实验结果表明,该模糊同步方法对于满足GLCF的所有混沌系统均适用。Generalized Lorenz system(GLS) contains the classical Lorenz system and infinite chaotic systems which are similar in structure but not topologically equivalent with Lorenz system.The system structure of generalized Lorenz canonical form(GLCF) is reconstructed based on T-S model.Then using Lyapunov stability theory and feedback synchronization concept,the reconstructed systems achieve synchronization.Moreover to the error system with the decay rate α,sufficient conditions of global asymptotic stability are given.Simulation researches based on LMI method for unified chaotic system and extended Liu system which are typical GLS show that the fuzzy synchronization method proposed is fit for all chaotic systems satisfying GLCF.

关 键 词：广义Lorenz系统 混沌同步 T-S模型 模糊建模 模糊控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]