一般非线性离散系统P-D型迭代学习收敛性研究

Study for Convergence of Open-closed-loop P-D-type Iterative Learning Control of Nonlinear Discrete Systems

针对非线性离散系统的控制问题,介绍了当前的研究现状,分析了开环迭代学习控制的不足,将某一类的非线性离散系统推广到了一般的非线性离散系统,对于一般的非线性离散系统,改变了以往只能借助前次的运行信息,提出了基于当前误差和前次运行误差信息的P-D型开闭环迭代学习控制律,使得对系统运行信息的利用更加充分、准确。此外,利用λ范数和归纳法给出了该学习律收敛的充分条件,证明了它的收敛性。仿真结果表明了它的有效性。

For the control problem of nonlinear discrete systems, this paper describes the status of current research and analyzes the deficiency of open-loop iterative learning controller. In this paper, a class of nonlinear discrete systems will be extended to the general nonlinear discrete systems. To the general nonlinear discrete systems, a open-closed-loop P-D-type iterative learning controller which based on current and last output error instead of last output error only is proposed. It makes use of information on system operation more fully and accurately. Besides, based on norm of k and mathematical induction, its sufficient condition for convergence is given. Simulation results show that it is efficient.