Optimal selection of the forgetting matrix into an iterative learning control algorithm
Optimal selection of the forgetting matrix into an iterative learning control algorithm
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DOI：
10.1109/tac.2005.860232
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发表时间：
2005-06
影响因子：
6.8
通讯作者：
S. Saab
中科院分区：
文献类型：
--
作者：
S. Saab
推导了一种基于最小化输入误差协方差矩阵的递归优化算法，用于生成任意相对度线性离散变系统的p型迭代学习控制的最优遗忘矩阵和学习增益矩阵。这个注释表明，轨迹的有界性和输出跟踪都不需要遗忘矩阵。特别地，证明了在随机干扰存在的情况下，所有学习迭代的最优遗忘矩阵为零。此外，由此产生的最优学习增益保证了轨迹的有界性以及在任意相对程度的测量噪声存在下的均匀输出跟踪。
A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the optimal forgetting matrix and the learning gain matrix of a P-type iterative learning control (ILC) for linear discrete-time varying systems with arbitrary relative degree. This note shows that a forgetting matrix is neither needed for boundedness of trajectories nor for output tracking. In particular, it is shown that, in the presence of random disturbances, the optimal forgetting matrix is zero for all learning iterations. In addition, the resultant optimal learning gain guarantees boundedness of trajectories as well as uniform output tracking in presence of measurement noise for arbitrary relative degree.