控制方向未知的时变不确定系统的重复控制

摘要

The paper studies the repetitive control of a class of nonlinear system with unknown time-varying parameters and unknown control direction.The Lyapunov functions used in the paper relate not only to the present parameter estimation errors,but also to the previous parameter estimation errors.A repetitive control law is presented by using the Lyapunov functions combined with the Nussbaum-type functions.Although in this method no saturation control is used,the tracking errors in the closed-loop converge to zero on the interval of repetition.Finally,a simulation example is presented to validate the effectiveness of the proposed method.%本文考虑一类具有未知时变参数并且控制方向未知的非线性系统的重复学习控制.针对重复学习控制的特点,所构造的李亚普诺夫函数不仅与当前参数估计误差有关,也与前一次参数估计误差有关.基于该李亚普诺夫函数,结合Nussbaum类型函数,提出了控制方向未知的系统的重复学习方法.该方法不采用饱和控制,但能保证在闭环系统中跟踪误差在重复区间上一致收敛于零.最后,一个仿真例子说明了该方法的可行性.