This article develops iterative machine learning (IML) for output tracking. The inputoutput data generated during iterations to develop the model used in the iterative update. The main contribution of this article to propose the use of kernel-based machine learning to iteratively update both the model and the model-inversion-based input simultaneously. Additionally, augmented inputs with persistency of excitation are proposed to promote learning of the model during the iteration process. The proposed approach is illustrated with a simulation example. §1. IntroductionIterative learning methods, initially developed in e.g.,, 1)-3) improve the outputtracking performance by correcting the input based on the measured tracking error. For example, iterative control has led to some of the highest precision for output tracking, e.g., in scanning probe microscopy as demonstrated in, e.g.,. 4)-10) Note that sets of learned trajectories can be used to enable tracking of other trajectories, e.g., by designing the feedforward control input using pre-specified basis functions e.g., using polynomial functions 11) or rational functions of the reference trajectory. 12) Similarly, new desired output can be generated by considering different combinations of previously-learned output segments 13) and the feedforward can be represented using radial basis functions that can be optimized for a range of task parameters. 14) This article proposes a kernel-based machine learning approach to use augmented inputs to iteratively learn not just the inverse input u d needed to track a specified output y d but to also use the data acquired during the iteration process to to estimate both (i) the modelĝ (and its inverse) for the control update, as well as (ii) the model uncertainty needed to establish bounds on the iteration gain for ensuring trackingerror reduction..Conditions for convergence of iterative methods have been well studied in literature, e.g.,. 15)-24) For example, the need to invert the system g to find the perfect input u d for tracking a desired output y d has motivated the use of the inversê g −1 of the known modelĝ of the system g in early iterative control development. 3) Since convergence depends on the size of modeling error, improvements of the model through parameter adaptation with data acquired during the iteration was studied in, e.g., 25) for robotics application using a discrete-time implementation. Here, for each iteration step, the sampled input vector is mapped to the sampled output vector through a lower triangular matrix map. A stochastic version using such a lower-triangular map has been studied in. 26) Even in the ideal case with no mod- * ) S. Devasia is with the Mechanical Engineering Department, U.