具有初始状态不确定性的非线性系统脉冲补偿迭代学习控制
Pulse compensated iterative learning control to nonlinear systems with initial state uncertainty
摘要点击 1865  全文点击 1192  投稿时间:2012-05-08  修订日期:2012-07-02
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DOI编号  10.7641/j.issn.1000-8152.2012.8.LCTA120470
  2012,29(8):993-1000
中文关键词  迭代学习控制  非线性系统  脉冲补偿  初始状态不确定性  Lebesgue-p范数
英文关键词  iterative learning control  nonlinear systems  pulse compensation  initial state uncertainty  Lebesgue-p norm
基金项目  This work was supported by the National Natural Science Foundation of China (No. F030114-60974140).
作者单位E-mail
阮小娥 西安交通大学 数学与统计学院 wruanxe@mail.xjtu.edu.cn 
赵建永 西安交通大学 数学与统计学院  
中文摘要
      针对于具有初始状态不确定性的非线性时不变系统, 采用矩形脉冲信号补偿传统的比例微分型一阶和二阶迭代学习控制律. 在Lebesgue-p范数度量跟踪误差意义下, 利用卷积的推广的Young不等式分析学习控制律的跟踪性能. 分析表明, 在适当选取比例学习增益, 微分学习增益和非线性状态函数的Lipschitz常数以保证收敛因子小于1的前提下, 渐近跟踪误差是由初始状态不确定性引起的, 而且可通过调节补偿因子予以消减. 数值仿真验证了补偿策略的有效性和理论分析的正确性.
英文摘要
      A type of rectangular pulse is adopted to compensate for conventional proportional-derivative-type firstorder and second-order iterative learning controllers of nonlinear time-invariant systems with initial state uncertainty. The tracking error is measured in the form of Lebesgue-p norm and the tracking performance is analyzed by the technique of generalized Young inequality of convolution integral. The analysis shows that the asymptotical tracking error is incurred by the initial state uncertainty and can be eliminated by tuning the compensation gain in the presuppose that the proportional and derivative learning gains together with the Lipschitz constant of the nonlinear state function are properly chosen to guarantee that convergence factor is less than one. Numerical simulations exhibit the validity of the theoretical derivation and the effectiveness of the compensation strategy.