对一类非严格重复系统的两种基于二阶内模的迭代学习控制器设计

通过对系统中的不确定参数建立迭代域上的二阶内模来研究一类非线性连续时间系统的非严格重复性，并依照内模原理提出了两种基于二阶内模的参数迭代学习控制器：二阶迭代学习控制器和平行迭代学习控制器．本文分别使用不同的Lyapunov函数，证明了两种控制器在各自的可行范围内都可以保证系统的跟踪误差收敛．通过对这两种学习机制的比较分析，说明了平行迭代学习控制设计的合理性．两个数值仿真不仅证实了两种算法的有效性，也展示了平行迭代学习控制器更好的收敛特性．

Two Types of Second-Order Internal Model Based Iterative Learning Controller Design for a Class of Non-Repetitive Systems

The paper is devoted to study non-repetitiveness for a class of nonlinear continuous-time systems by building second-order internal model in iteration domain for system＇s uncertainty parameters. According to internal model principle, two types of second-order internal model-based parametric iterative learning controllers are proposed, which are second-order iterative learning controller and parallel iterative learning controller. Utilizing different Lyapunov functions, the paper proves that tracking error convergence can be guaranteed by each designed controller within its own feasible domain. By comparison of their learning mechanisms, the design rationality of parallel iterative learning controller is clarified. Two numerical examples not only verify the effectiveness of both algorithms, but also show better convergent performance using parallel iterative learning controller.