Iterative learning control (ILC) is a control strategy for repetitive tasks wherein information from previous runs is leveraged to improve future performance. Optimization-based ILC (OB-ILC) is a powerful design framework for constrained ILC where measurements from the process are integrated into an optimization algorithm to provide robustness against noise and modelling error. This paper proposes a robust ILC controller for constrained linear processes based on the forward-backward splitting algorithm. It demonstrates how structured uncertainty information can be leveraged to ensure constraint satisfaction and provides a rigorous stability analysis in the iteration domain by combining concepts from monotone operator theory and robust control. Numerical simulations of a precision motion stage support the theoretical results.

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We propose an optimization-based method to improve contour tracking performance on precision motion stages by modifying the reference trajectory, without changing the built-in low-level controller. The position of the precision motion stage is predicted with data-driven models. First, a linear lowfidelity model is used to optimize traversal time, by changing the path velocity and acceleration profiles. Second, a non-linear high-fidelity model is used to refine the previously found timeoptimal solution. We experimentally demonstrate that the method is capable of improving the productivity vs. accuracy trade-off for a high precision motion stage. Given the data-based nature of the models used, we claim that the method can easily be adapted to a wide family of precision motion systems.

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