Iterative Model Learning and Dual Iterative Learning Control: A Unified Framework for Data-Driven Iterative Learning Control

Accurate reference tracking is essential in control tasks, and, in repetitive systems, Model-Based Iterative Learning Control (MB-ILC) is a standard solution. However, MB-ILC suffers from two downsides: MB-ILC not only requires prior model information but also learning parameters that have to be manually tuned, which poses an inherent design effort. To overcome the requirement of model information, Data-Driven ILC (DD-ILC) methods have been proposed which, nonetheless, still require manual parameter tuning and also do not preserve the modularity and theoretical guarantees of MB-ILC. To overcome these issues, we propose the two frameworks of Iterative Model Learning (IML) and Dual Iterative Learning Control (DILC). The IML framework enables iterative learning of unknown dynamics in repetitive systems using input/output trajectory pairs, and we formally prove the duality of IML and ILC, i.e., an IML system is equivalent to an ILC system with a trial-varying reference and trial-varying but known dynamics. Hence, existing MB-ILC methods can be utilized within the IML framework to learn models of unknown dynamics. The proposed DILC framework combines IML and MB-ILC to modularly employ various MB-ILC methods and to relieve them of requiring prior model information. To overcome the need for manual parameter tuning, we propose systematic self-parametrization schemes that enable the proposed methods to self-reliantly determine necessary learning parameters. We formally investigate the convergence of the proposed methods, and both IML and DILC are validated in extensive simulations and real-world experiments. A comparison using simulations demonstrates that by means of self-parametrization the proposed DILC framework significantly outperforms two state-of-the-art DD-ILC methods.