华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (1): 52-61.

• 应用数学与基础数学 • 上一篇    下一篇

一个新的类 Lorenz 系统的控制与同步（英）

张青,舒永录,张万欣   

  1. 重庆大学 数理学院, 重庆400044
  • 收稿日期:2009-04-14 修回日期:2009-06-16 出版日期:2010-01-25 发布日期:2010-01-25
  • 通讯作者: 张青

Controlling and synchronization of a new Lorenz-like chaotic system

ZHANG Qing,SHU Yong-lu,ZHANG Wan-xin   

  1. College of Mathematics and Physics, Chongqing University, Chongqing 400044, China
  • Received:2009-04-14 Revised:2009-06-16 Online:2010-01-25 Published:2010-01-25
  • Contact: ZHANG Qing

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摘要： 首先, 利用 Backstepping 方法设计了简单的控制器将系统控制到不稳定的平衡点(0,0,0), 相空间中任一指定点 (0,0,1+b+p(1-p)) (0<p<1),以及实现利用第一个状态变量跟踪任意指定的函数 r(t). 其次,在假设有一个参数未知的条件下, 设计了一个单向偶合格式和未知参数的自适应律,使得该系统与其自身达到全局完全同步. 用Lyapunov 函数方法从理论上证明了设计的正确性,并用 Matlab 作了数值模拟说明设计的可行性.

关键词: 混沌, 反演控制, 自适应同步, 混沌, 反演控制, 自适应同步

Abstract: By using the backstepping design method we formulated a simple controller to control the system to its unstable equilibrium (0,0,0), any point of the form (0,0,1+b+p(1-p))(0<p<1) in phase space, and forced the first state variable to trace arbitrary given function r(t). Suppose one parameter was unknown, we proposed a unidirectional coupled scheme and a parameter update role to assure the new Lorenz-like system to globally synchronize with a copy of itself. We presented a rigorous proof of our design by constructing proper Lyapunov function. Numerical simulations using Matlab were presented to show the feasibility of our design.

Key words: backstepping control, adaptive synchronization, chaos, backstepping control, adaptive synchronization

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