一类二阶时变非线性系统的混合自适应重复学习控制

针对含有时变和时不变未知参数的二阶非线性系统，结合Backstepping方法．提出了一种新的自适应重复学习控制方法，可处理参数在一个未知紧集内周期性快时变的非线性系统．通过引入参数周期自适应律．设计出的自适应控制策略．使跟踪误差平方在一个周期上的积分范敷渐近收敛于零．通过构造Lyapunov函数．给出了闭环系统收敛的一个充分条件．

Adaptive repetitive learning control for a class of second order nonlinear time-varying systems with mixed parameters

A novel adaptive repetitive learning control for second-order nonlinear systems with time-varying and time-invariant parameters is proposed by using the Baekstepping approach. It can be applied to the time-varying parametric uncertainty systems with an unknown compact set, which are non-vanishing, rapid time-varying, and periodic and where the prior knowledge is the periodicity only. A periodic mixed adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm. Also, a sufficient condition for the convergence of the method is given. A simulatioin example illustrates the effectiveness and the feasibility of the proposed method.