Tensor techniques for iterative learning control of a free-electron laser

An iterative learning control (ILC) algorithm reduces repetitive control errors to a desired trajectory within the same repeated task. This paper considers an alternative ILC representation based on a tensor representation. Hereby a decoupling of static and dynamic parts of each calculated ILC matrix leads for computational reasons to a reduction by an order of magnitude. Based on such tensor representation the Norm Optimal ILC is compressed to a Norm Optimal Tensor ILC. The reduced number of elements to store the ILC parameter in this approach simplifies the calculation, especially for high sampled datasets and therefore long trajectories. The resulting algorithm is implemented at FLASH, a free electron laser facility, highly suitable for this approach.