一种基于高阶内模的新型自适应迭代学习算法  

A New Adaptive Iterative Learning Algorithm Based on a High-Order Internal Model

作　　者：张国山 李思祺 Zhang Guoshan;Li Siqi(School of Electrical and Information Engineering,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学电气自动化与信息工程学院,天津300072

出　　处：《天津大学学报（自然科学与工程技术版）》2022年第5期480-488,共9页Journal of Tianjin University：Science and Technology

基　　金：国家自然科学基金资助项目(62073237)。

摘　　要：本文针对一类含多个时间迭代变化参数控制方向未知的非线性离散时间系统的输出跟踪问题,提出了一种基于高阶内模的新型自适应迭代学习算法.假设多个时间迭代变化参数由不同的高阶内模所生成,本文所提出的算法借鉴了模型预测控制的思想,通过构建预测输入,将获得的当次迭代预测跟踪误差作为先验知识,应用到系统输入的控制律的设计中,从而在预测跟踪误差的基础上进一步缩小系统的跟踪误差.相较于基于高阶内模的传统迭代学习算法,大幅度缩减了系统的输出跟踪误差,明显地提高了跟踪精度.此外,由于预测跟踪误差作为先验知识参与了系统输入控制律的设计,该方法对于系统扰动和输出噪声具有较强的鲁棒性.通过Lyapunov稳定性理论,证明了该方法下系统跟踪误差的收敛性和所提算法的优越性.通过两组仿真算例,考虑在控制方向已知和未知两种情况下,和两种基于高阶内模的已有迭代学习算法进行了对比,验证了理论结果.In this paper,a new adaptive iterative learning algorithm based on a high-order internal model is proposed.The algorithm is applied to the output tracking problem of a class of nonlinear discrete-time systems with multiple time-iteration-varying parameters and unknown control directions.Assuming that multiple time-iteration-varying parameters are generated by different high-order internal models,the proposed algorithm draws on the idea of model predictive control.Through the construction of predictive input,the predictive tracking error obtained in the current iteration is used as a priori knowledge for system input control law design.This has the effect of further reducing the tracking error of the system on the basis of predictive tracking error.Compared with the traditional iterative learning algorithm based on a high-order internal model,the output tracking error of the system is greatly reduced,and the tracking accuracy is evidently improved.In addition,as predictive tracking error is involved in the design of the input control law as a priori knowledge,the method is robust to system disturbance and output noise.Through the Lyapunov stability theory,the convergence of the system tracking error and the superiority of the proposed method are proved.Through two groups of sample simulations,and considering the two cases of known and unknown control direction,the theoretical results are verified by comparison with two existing iterative learning algorithms based on a high-order internal model.

关 键 词：自适应迭代学习控制 高阶内模 非线性离散时间系统 时间迭代变化参数 

分 类 号：TK13[动力工程及工程热物理—热能工程]