一类非参数不确定系统的自适应重复学习控制

Adaptive repetitive learning control for a class of nonparametric uncertain systems

中文关键词  重复学习控制  自适应控制系统  非参数不确定性  Lyapunov方法

英文关键词  repetitive learning control  adaptive control systems  nonparametric uncertainties  Lyapunov methods

中文摘要

      本文针对一类非参数不确定系统提出一种全限幅自适应重复学习控制方法. 利用期望轨迹的周期特性, 构 造周期性期望控制输入, 并基于Lyapunov方法设计自适应重复学习控制器, 实现系统对周期性期望轨迹的高精度跟 踪, 且无需已知非参数不确定性的上界. 设计全限幅学习律估计未知的期望控制输入, 保证估计值被限制在指定的 界内. 同时, 通过构造完全平方式消除部分误差相关项, 控制器设计中可避免使用符号函数, 从而抑制控制器抖振问 题. 最后, 基于Lyapunov方法对误差收敛性进行了分析, 并通过仿真对比验证本文所提方法的有效性.

英文摘要

      In this paper, a fully saturated adaptive repetitive learning control (ARLC) scheme is proposed for a class of nonparametric uncertain systems. A periodic desired control input is constructed by using the periodic characteristic of the desired trajectory, and an adaptive repetitive learning controller is designed based on the Lyapunov methods to achieve the high-precision tracking of the periodic desired trajectory without knowing the upper bound of the nonparametric uncertainties in prior. Then, a fully saturated repetitive learning law is designed to estimate the unknown desired control input, such that the estimated value can be confined within a specified region. By completing the squares to eliminate some error-related terms, the signum function can be avoided in the controller design, and thus the chattering problem of the controller is suppressed. Finally, the error convergence performance of the proposed ARLC scheme is analyzed through the Lyapunov methods, and comparative simulations are provided to verify the effectiveness of the proposed scheme.