Tom Oomen

Research on Iterative Learning Control

General theory

Iterative Learning Control is an extremely interesting control strategy that can deliver exceptional performance for many systems by compensating all predictable components in the error signal. The main idea is to learn from previously made errors. ILC is a fairly well-developed approach and we present a fairly complete theoretical overview, algorithms, and design framework in

  • M.Sc. Course: Capita Selecta in Control: Iterative Learning Control - TU Eindhoven

  • Post Academic Course: Advanced Feedforward Control - The High Tech Institute, organised by Tom Oomen and Maarten Steinbuch

Besides new developments on the general theory of ILC that we have investigated in our research and present in our education, some specific results are outlined below.

ILC for sampled-data systems: intersample behavior

On the research side, we are investigating several aspects, including ILC for sampled-data systems. ILC is traditionally implemented in a digital computer environment, i.e., in discrete time. In contrast to standard feedback control where disturbance attenuation is limited due to the Bode sensitivity integral, ILC can attenuate disturbances up to the Nyquist frequency. As a result, it achieves almost perfect performance… at the sampling instants. Our research hypothesis was that pushing the performance at the sampling instants this far might go at the expense of the intersample behavior (actually, the main reason that led to this reason was a disagreement on the notion of lifted system between Jeroen van de Wijdeven and myself: the notion of lifted system in ILC seemed fairly different from the usual definition in LPTV and sampled-data systems - this has also been settled, see my lecture notes!). To investigate this, we developed a sampled-data/multirate ILC framework, which is documented in

Low-order ILC for reduced computation time

In developing the approaches above we realised the norm-optimal ILC framework involves a huge computational load. When we started thinking about this further, it appeared that one is actually solving a large LQ problem by casting it as a matrix least-squares problem. In feedback control design, similar problems are being solved through Riccati equations. This has led us to develop new algorithms for ILC based on Riccati equations, which is documented in

ILC for inferential systems

A very similar problem arises in inferential control, where one also cannot measure the performance variables directly. Instead, in many cases one can measure the “performance” after a task has been performed, e.g., by inspecting the final product. This leads to a batch-to-batch operation of ILC. We have recently shown that a direct implementation of an ILC controller controller leads to a “fight” between the feedback controller (operating in the “time” domain) and the iterative learning controller (operating in the “iteration” domain). In a 2D system theoretic setting, it is shown that this situation in fact is often internally unstable. The results are reported in, e.g.,

Data-driven ILC: removing the need for filter design

A key aspect in the above approaches is that these require an approximate model of the system to ensure convergence. Model errors can lead to divergence of the ILC algorithm, which in turn necessitates robustness, either through design or by pursuing a robust ILC approach. This observation has led us to develop data-driven ILC approaches that do not require any model for learning. Initial work in this direction is documented in

  • Data-Driven Optimal ILC for Multivariable Systems: Removing the Need for L and Q Filter Design
    Joost Bolder and Tom Oomen
    Submitted for publication

Iteratively learning the mathcal{H}_infty norm

Besides learning of the feedforward command signal for good servo performance, we have recently been investigating learning algorithms for learning the mathcal{H}_infty norm of multivariable systems. The main motivation for doing this originates from uncertainty modeling for robust control, where an accurate bound on the model uncertainty is required. Results of this research are reported in

Further extensions

Several further extensions have been made, including

  • ILC with basis functions. A key advantage of ILC is that it typically results in superior performance for control systems that is very hard to achieve using other techniques. The price to pay is that the taks must be exactly repetitive. Unfortunately, this is severely restrictive for many industrial systems. Therefore, we are developing a new approach to extend the flexibility of ILC while retaining the ultra high performance. The main idea is to use basis functions in ILC.

Due to the close connection to feedforward, these extensions and many others are described on the research page on advanced and iterative feedforward control. We recommend to continue reading there!


The success of all the above work is due to many collaborations, both in academia and industry. Most of these collaborators are mentioned as co-authors, and their contribution is gratefully acknowledged.

Note that all figures shown on this page can be found in the mentioned papers. Please follow the guidelines regarding copyright and references when citing these.