北京航空航天大学学报 ›› 2011, Vol. 37 ›› Issue (4): 452-457.

• 论文 • 上一篇    下一篇

非完整链式系统的全局连续K指数镇定

李明军, 马保离   

  1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191
  • 收稿日期:2010-05-11 出版日期:2011-04-29 发布日期:2011-04-29
  • 作者简介:李明军(1981-),男,湖南永兴人,博士生,limingjun_8888@163.com.
  • 基金资助:

    国家自然科学基金资助项目(60874012)

Global K-exponential stabilization of nonholonomic chained systems by continuous feedback

Li Mingjun, Ma Baoli   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2010-05-11 Online:2011-04-29 Published:2011-04-29

摘要: 为非完整链式系统提出了两种全局连续反馈控制律,即连续时变反馈控制律和动态时不变反馈控制律.第1种控制律通过引入一个与状态初值有关的指数衰减项,来保证控制律的连续性和渐近性.第2种控制律通过引入一个可自由设定初值的辅助状态,来保证系统的可控性以及控制律的连续性和渐近性.这两种控制律可以保证系统所有状态以指数速度渐近地、连续地收敛到原点,克服了以往控制律不能同时具有连续性、渐近性和指数收敛速度的缺陷.所得控制律应用于移动机器人系统和一个4维链式系统的镇定,仿真结果表明:状态轨迹和控制轨迹的光滑度和收敛速度都要优于以往控制律.

Abstract: Two global continuous feedback control laws were proposed to stabilize nonholonomic chained systems, namely, the continuous time-varying feedback control law and the dynamic time-invariant feedback control law. The first control law achieved continuity and asymptoticality by using an exponential decay term related to the initial state values, while the second achieved controllability, continuity and asymptoticality by setting the initial value of the introduced assistant state variable. The two control laws could guarantee that all the states converged to zero continuously and asymptotically at exponential rates, which overcame the short-comings that the previous control laws could not achieve continuity, asymptoticality and exponential rates at the same time. The proposed control laws are applied to the mobile robot and a four-dimension chained system. The simulation results show that the smoothness and convergence rates of the state/control trajectories are better than the previous works.

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