高阶相对度线性时不变系统的迭代学习控制  

Iterative Learning Control for Linear Time-invariant Systems with Higher-order Relative Degree

作　　者：阮小娥[1] 王杰[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《应用数学学报》2014年第6期1077-1092,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(F030114;60974140)和(F030114;61273135)资助项目

摘　　要：本文针对于一类具有高阶相对度的线性时不变系统,提出了两种相对度关联的高阶导数型迭代学习控制机理.利用分部积分法和卷积的Young不等式,推演Lebesgue-p范数度量意义下两种高阶导数型迭代学习控制律的单调收敛性.进一步,针对于系统存在初始状态漂移情形,本文引入了多矩形脉冲补偿机制,以抑制初始状态漂移引起的跟踪误差,给出了增强抑制作用的补偿增益的调整方法.数值仿真展示了控制策略的有效性.In this paper, two types of relative degree related higher-order derivative-type iterative learning control schemes are developed for a class of linear time-invariant （LTI） systems with higher-order relative degree. By means of the integral method by parts and the generalized Young inequality of convolution integral, monotone convergence of the proposed iterative learning control strategies is derived in the sense that the tracking error is measured in the form of Lebesgue-p norm. Besides, for the system with initial state shift, a form of multi-pulse compensation is utilized for the purpose of suppressing the tracking error incurred by the initial state shift and the tunning manner of the compensation gains is discussed for enhancing the suppresion. The validity and effectiveness of the proposed strategies are exhibited by numerical simulations.

关 键 词：迭代学习控制 高阶相对度 单调收敛性 Lebesgue-p范数 多矩形脉冲补偿 

分 类 号：O212.7[理学—概率论与数理统计]