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更一般高阶非完整系统的指数调节

高芳征1,尚艳玲2,袁付顺1   

  1. 1. 安阳师范学院数学与统计学院, 安阳 455002; 2.安阳师范学院计算机教学部,  安阳 455002
  • 收稿日期:2011-03-07 出版日期:2012-02-25 发布日期:2012-04-26

高芳征,尚艳玲,袁付顺. 更一般高阶非完整系统的指数调节[J]. 系统科学与数学, 2012, 32(2): 149-160.

GAO Fangzheng, SHANG Yanling, YUAN Fushun. EXPONENTIAL REGULATION FOR MORE GENERAL HIGH-ORDER NONHOLONOMIC SYSTEMS[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(2): 149-160.

EXPONENTIAL REGULATION FOR MORE GENERAL HIGH-ORDER NONHOLONOMIC SYSTEMS

GAO Fangzheng1 , SHANG Yanling2 , YUAN Fushun1   

  1. 1.(School of Mathematics and Statistics, Anyang Normal University, Anyang 455002; 2.Teaching Department of Computer, Anyang Normal University, Anyang 455002
  • Received:2011-03-07 Online:2012-02-25 Published:2012-04-26
研究了一类更具有一般性的强漂移高阶非完整系统的指数调节问题. 首先通过指数形式的input-state-scaling不连续变换将原$x$子系统的指数调节问题转化为变换后$z$子系统的镇定问题,  并有效克服$x$子系统在控制输入$u_{0}=0$时不能控的问题.然后基于 ``加幂积分器" 反推方法设计鲁棒控制器, 在新的切换策略下,使闭环系统状态指数收敛到零点.仿真例子验证了所提方法的有效性.
The problem of exponential regulation is addressed for a class of more general uncertain high-order nonholonomic systems with strong nonlinear drifts. First of all, a discontinuous input-state-scaling transformation in exponential form is introduced to convert exponential regulation of the x subsystem into the stabilization problem of the z subsystem, and hence the phenomenon of uncontrollability in u0 = 0 is avoided. Then, by using the method of adding a power integrator, a state feedback controller is successfully designed. Based on a novel switching strategy, the proposed controller guarantees that the closed-loop system state exponentially converges to zero. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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