研究一类线性不确定系统的鲁棒D型迭代学习控制问题. 首先针对一类线性标称控制对象, 建立其迭代学习控制的二维模型; 然后基于获得的二维模型, 利用二维系统稳定性理论, 获得系统在迭代初态与期望初态一致和不一致两种情形下的D型迭代学习控制律的存在条件和设计方法; 进一步, 将所得结果推广至控制对象包含不确定性的情形. 所得结果以线性矩阵不等式(LMI)的形式给出, 可以方便地利用Matlab中的LMI工具箱求解. 最后, 数值仿真实例验证了本文所提方法的有效性.

This paper is concerned with a robust D-type iterative learning control (ILC) method for a class of linear uncertain systems. First, a 2D model of ILC
for a linear normal control plant is established. Next, based on 2D model and using the 2D systems stability theory, the existence condition and method of designing a robust D-type iterative learning controller for such  control system are derived with variable initial conditions. Furthermore, the results are extended to control lant with uncertainties. All the results are obtained in terms of LMI, which can be easily obtained by Matlab's LMI toolbox. Finally, a numerical example demonstrates the validity of this approach.