Robust data-driven frequency-domain-based ILC designs for non-repetitive linear discrete-time systems

This article introduces two robust data-driven iterative learning control (ILC) laws for linear discrete-time systems (LDTSs) with single input and single output (SISO), considering non-repetitive uncertainties in initial conditions, reference trajectories, and external disturbances. The proposed robust ILC laws are developed in frequency domain by using an innovative adaptive Fourier decomposition (AFD) method to approximate the unknown transfer function. They are entirely data-driven in the sense that the input and output (I/O) data of the controlled LDTS are utilized only without requiring any model knowledge beyond the minimum phase feature of the system. Consequently, the ILC tracking errors can be confined within a bounded region whose size can be adjusted by a suitable selection of learning gains. Notably, as the iteration-variant initial conditions, reference trajectories, and system disturbances are progressively repetitive, the designed ILC schemes can ultimately achieve perfect tracking of reference trajectories. Numerical simulations validate the presented robust data-driven ILC laws.