DATA-BASED NORM-OPTIMAL ITERATIVE LEARNING CONTROL VIA GAUSSIAN PROCESS REGRESSION\ast

Norm-optimal iterative learning control (NOILC) is effective for repetitive systems in achieving the monotonic decrease of the tracking error with respect to a specified trajectory. However, for classical NOILC, the model information is required, which contradicts the essential data-based characteristic for iterative learning control. Inspired by this contradiction, the current paper aims to establish a data-based design and analysis framework for NOILC, focusing on uncertain linear systems without system constraints. A Gaussian process regression (GPR)-based approach is leveraged to develop a virtual input-output relationship from only the collected system data, with which the design of NOILC can be accomplished without any model information. The monotonic convergence analysis of the proposed GPR-based NOILC is implemented such that the robust tracking task can be achieved in the presence of iteration-varying initial state shifts and disturbances, and the boundedness of all system trajectories can be ensured simultaneously. An example is also included to validate the effectiveness and robustness of the presented GPR-based NOILC methods.