基于边界层的一类不确定系统的迭代学习控制

Boundary Layer-Based Iterative Learning Control for a Class of Uncertain Systems

针对一类具有任意初态和非周期有界扰动的不确定非线性时变系统,提出一种基于边界层的迭代学习控制方法,将边界层设计成一个具有剩余宽度的指数衰减函数,通过边界层把任意初态问题转换为零初值迭代学习问题.针对周期和非周期不确定性扰动,分别设计周期项的学习律和非周期项的边界学习律,然后在此基础上给出了迭代学习控制算法.文中给出了相关定理,并应用类Lyapunov方法给出了定理的详细证明.仿真结果表明,所提出的算法是有效的,轨迹跟踪误差能收敛到边界层.

For a class of uncertain nonlinear time-varying systems with arbitrary initial states and aperiodic bounded disturbance,an iterative learning control（ ILC） method on the basis of boundary layer is presented. In this method,boundary layer is designed as a decaying exponential function with residual width,the arbitrary initial state problem of ILC is transformed into a zero initial state problem by the designed boundary layer,and learning laws of periodic and aperiodic terms are designed for periodic and aperiodic disturbances,respectively. On the basis of these two laws,an ILC algorithm is presented,and the corresponding theorem is given with detail proof through Lyapunov-like approach. Simulated results show that the proposed algorithm is effective and is capable of converging trajectory tracking errors to boundary layer.