Data-driven ILC algorithms using AFD in frequency domain for unknown linear discrete-time systems

Frequency‐domain‐based iterative learning control utilizing n‐best adaptive Fourier decomposition for nonrepetitive unknown iteration‐independent and iteration‐varying discrete time‐delay systems

“…Then, the convergence analysis utilizing the extended anticipatory ILC law (16) or (18) is presented in the following Theorem 1.…”

“…Theorem 2. For the LDTD system (23) with Assumptions 3 and 4, utilize the extended anticipatory ILC law (16) or (18). If the learning gains 𝛼 and 𝛽 in (16) or (18) make that…”

“…To facilitate the applications of the bound to the standard remainder $$$ {R}_{\tilde{G}}\left({z}^{-1},M\right) $$$ in subsequent ILC designs, it is demonstrated in Reference 18 that $$$ \left\Vert {R}_{\tilde{G}}\left({z}^{-1},M\right)\right\Vert \le \frac{L_g}{\sqrt{M}} $$$ is equivalent to $$$$ \left|{R}_{\tilde{G}}\left({z}^{-1},M\right)\right|\le \frac{L_g}{\sqrt{M}}.. $$$$ Letting $$$ \tilde{G}\left({z}^{-1}\right)=\hat{G}\left({z}^{-1},\tilde{N}\right) $$$ and combining (14) with (11), it yields …”

“…Recently, a novel adaptive Fourier decomposition (AFD) that is used to identify the transfer function has been introduced in the frequency-domain-based ILC design. 17,18 However, the AFD approximation method in Reference 17 is based on support vector machine theory, which leads to the convergence of the ILC tracking error in a statistical learning sense. The convergence probability of the ILC tracking error depends on the AFD approximation error to the transfer function for linear discrete-time systems.…”

“…The objective of this paper is to develop a faster, fully data‐driven ILC algorithm that is based on a frequency domain identification technique to relax the requirement of uncertainty for non‐repetitive LDTD systems in the frequency domain. Recently, a novel adaptive Fourier decomposition (AFD) that is used to identify the transfer function has been introduced in the frequency‐domain‐based ILC design 17,18 . However, the AFD approximation method in Reference 17 is based on support vector machine theory, which leads to the convergence of the ILC tracking error in a statistical learning sense.…”