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Iterative learning control for one-dimensional fourth order distributed parameter systems


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This paper addresses the problem of iterative learning control algorithm for high order distributed parameter systems in the presence of initial errors. And the considered distributed parameter systems are composed of the one-dimensional fourth order parabolic equations or the one-dimensional fourth order wave equations. According to the characteristics of the systems, iterative learning control laws are proposed for such fourth order distributed parameter systems based on the P-type learning scheme. When the learning scheme is applied to the systems, the output tracking errors on L 2 space are bounded, and furthermore, the tracking errors on L 2 space can tend to zero along the iteration axis in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.


首次将迭代学习控制设计应用到四阶分布参数系统上, 该类分布参数系统由一维四阶抛物型方程或一维四阶波方程构成。针对文中的四阶抛物型和四阶双曲型两类系统, 构建得到通用的迭代学习控制器和收敛性条件。当学习控制律作用于系统时, 若迭代系统存在初值偏移, 则L2意义下的输出跟踪误差有界, 且该界与初值偏移的界有关;若迭代系统无初值偏移, 则L2意义下的输出跟踪误差沿迭代轴方向一致收敛于零。

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Correspondence to Qin Fu.

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Fu, Q., Gu, P. & Wu, J. Iterative learning control for one-dimensional fourth order distributed parameter systems. Sci. China Inf. Sci. 60, 012204 (2017). https://doi.org/10.1007/s11432-015-1031-6

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  • P-type learning scheme
  • iterative learning control
  • distributed parameter systems
  • fourth order parabolic equation
  • fourth order wave equation


  • P型学习律
  • 迭代学习控制
  • 分布参数系统
  • 四阶抛物型方程
  • 四阶波方程