Accurate reference tracking is essential in control tasks in a variety of applications, and, in repetitive systems, model-based Iterative Learning Control (ILC) is a standard solution that is underpinned by formal stability and convergence guarantees. To overcome the limitations of model-based ILC design, data-driven ILC methods have been introduced which lead to a patchwork of several, very different approaches that do not preserve the modularity and theoretical guarantees of the many, well-established model-based ILC methods. We, for the first time, propose a unifying framework for data-driven ILC that preserves the modularity and formally proven properties of model-based ILC. Specifically, we propose 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. We formally prove the duality between 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. We further provide generic conditions to guarantee the convergence of the model and prove the duality of monotonic convergence in ILC and IML. This duality allows arbitrary, established, model-based ILC methods to be effectively applied within the IML framework to learn models of unknown dynamics. Unlike existing data-driven ILC approaches which only combine specific model learning schemes with specific model-based ILC approaches, the proposed DILC framework combines IML with model-based ILC such that established, model-based ILC methods can be arbitrarily combined for simultaneous model and control learning with a formally proven separation principle. The proposed DILC is a unified framework for data-driven ILC that not only relieves model-based ILC of a priori model requirement but also preserves the modularity and theoretical guarantees of model-based ILC. Both IML and DILC are validated by extensive simulations and real-world experiments.

This work addresses the problem of reference tracking in autonomously learning agents with unknown, nonlinear dynamics. Existing solutions require model information or extensive parameter tuning, and have rarely been validated in real-world experiments. We propose a learning control scheme that learns to approximate the unknown dynamics by a Gaussian Process (GP), which is used to optimize and apply a feedforward control input on each trial. Unlike existing approaches, the proposed method neither requires knowledge of the system states and their dynamics nor knowledge of an effective feedback control structure. All algorithm parameters are chosen automatically, i.e. the learning method works plug and play. The proposed method is validated in extensive simulations and real-world experiments. In contrast to most existing work, we study learning dynamics for more than one motion task as well as the robustness of performance across a large range of learning parameters. The method’s plug and play applicability is demonstrated by experiments with a balancing robot, in which the proposed method rapidly learns to track the desired output. Due to its model-agnostic and plug and play properties, the proposed method is expected to have high potential for application to a large class of reference tracking problems in systems with unknown, nonlinear dynamics.