随机变批次长度的反馈辅助PD型量化迭代学习控制
作者:
作者单位:

1.北京化工大学;2.中国人民大学数学学院

作者简介:

通讯作者:

中图分类号:

TP273

基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目)


Feedback-assisted PD-type quantized iterative learning control with randomly iteration varying lengths
Author:
Affiliation:

1.Beijing University of Chemical Technology;2.School of Mathematics, Renmin University of China

Fund Project:

The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    本文针对离散线性系统,研究了批次长度随机变化的反馈辅助PD型量化迭代学习控制问题.考虑系统信号经量化后传输到控制器或执行器的情况,给出两种量化方案:跟踪误差信号量化和控制输入信号量化;基于这两种不同的量化信号,在批次长度和初始条件随机变化前提下设计了反馈辅助 PD 型迭代学习控制算法;采用扇形界的处理方法和堆积系统框架,推导了数学期望下的学习收敛条件:在误差信号量化情况下,所提控制算法可以保证跟踪误差渐近收敛到零;在控制输入信号量化情况下,所提控制算法能保证跟踪误差有界收敛.本文方法放宽了经典迭代学习控制中对重复系统批次长度和初始条件均为相同的要求.仿真示例对比验证了两种量化方案下所提方法的有效性和优越性.

    Abstract:

    The feedback-assisted PD-type quantized iterative learning control problem is studied for discrete linear systems with iteration-varying trial lengths in this paper.Considering that the system signal is transmitted to the controller or actuator after being quantized.Two quantization schemes are given:including tracking error signal quantization and control input signal quantization;In the case of iteration-varying trial lengths and iteration-varying initial state conditions,a feedback-assisted PD-type update law is developed based on the quantized signal.The learning convergence conditions under mathematical expectations are derived with the sector bound method and the lifting representation:tracking error signal quantization can obtain zero tracking error;while control input signal quantization only guarantee that the tracking error converges to a bound.The requirement is relaxed that all trial lengths and initialization condition must be the same for the classic iterative learning control.Simulation examples are provided to demonstrate the effectiveness and superiority of the proposed scheme under the two quantization schemes.

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历史
  • 收稿日期:2020-03-12
  • 最后修改日期:2020-06-02
  • 录用日期:2020-06-12
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