Iterative Learning Control for SO(2) Symmetric Systems

For realtime applications of Iterative Learning Controllers (ILC) runtime and memory usage are important issues. It is shown, that complexity of a Norm-Optimal Iterative Learning Controller can be significantly reduced by exploiting symmetries of the plant. Especially for the important class of SO(2) symmetric systems, explicit simplifications of the basic control algorithm by group transformations are given. These could be integrated in the framework of Norm-Optimal Tensor ILC. The example of the free-electron laser FLASH shows a relevant application area of symmetric ILC algorithm.