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针对一类含未知时变参数的满足线性增长条件的离散非线性系统,提出一种有限时间区间的轨迹跟踪参数自适应迭代学习控制(Iterative learning control,ILC)方案,讨论了该算法的收敛性以及利用遗忘因子提高收敛速度的问题。该方法利用离散时间自适应控制中的遗忘因子最小二乘法,在迭代域上构造新的参数自适应更新律和控制律,同时利用类Lyapunov函数证明跟踪误差在时间域上的逐点收敛、迭代域上的渐近收敛。给出两个仿真例子说明提出的参数自适应律与控制方法的有效性。
A class of discrete iterative learning control (ILC) scheme is proposed for a class of discrete nonlinear systems that satisfy the condition of linear growth with unknown time-varying parameters. The convergence of the algorithm As well as the use of forgetting factors to improve the convergence rate. This method uses the forgetting factor least square method in discrete-time adaptive control to construct a new parameter adaptive updating law and control law on the iterative domain. At the same time, the class Lyapunov function is used to prove the point-by-point convergence and iteration of the tracking error in the time domain Asymptotic Convergence on the Domain. Two simulation examples are given to illustrate the effectiveness of the proposed adaptive parameter law and control method.