LEARN is an acrynom for
It is a five-year project that started January 1, 2011 and will be finished December 31, 2015 and it is supported by a grant of 2.5 million Euros from the European Research Council, ERC. The project is carried out by a joint team from Division of Automatic control at Linköping Univerisity (LiU) and from the Division of Automatic control at the Royal Institute of Technology in Stockholm (KTH).
An outline of ideas in LEARN, along with some results from the first year is given in
EJC paper: Lennart Ljung, Håkan Hjalmarsson, and Henrik Ohlsson: Four encounters with system identification. European Journal of Control, 2011, Nr 5-6, pp 449-471.
The Principal Investigator is Lennart Ljung, LiU, and Håkan Hjalmarsson, KTH, is co-PI. The project is organized into five themes:
The development of convex and semidefinite programming has been booming in recent years, and has played a major role in several research communities. Convexification of estimation problems has been a very visible theme in the statistics community. However, such activities have not been particularly pronounced in the System Identification community which has largely been sticking to a maximum likelihood (or related) framework. It is perhaps symptomatic that some very recent and interesting applications of semidefinite programming techniques to system identification, have their origins in optimization rather than identification research groups. To be fair, it must be said that also research on subspace identification methods and attempts to work with predictors that are linear in the parameters, like LS Support Vector Machines and kernel-like techniques, could be seen as a convexification trend. There is thus a clear link to the research Theme IV. Another area that belongs to the state-of-the-art in this context is model reduction. Model reduction is closely related to System Identification, by its inherent system approximation feature. It is therefore interesting to follow convexification attempts for model reduction problems, and see if they have implications on the identification problem.
D. Eckhard and A.S. Bazanella and C.R. Rojas and H. Hjalmarsson Input design as a tool to improve the convergence of PEM Automatica Vol 49, pp 3282-3291.
We have shown that, for a general family of model structures for linear systems, adaptive experiment design asymptotically has the same accuracy as if complete knowledge of the true system was used in the experiment design.
Paper: http://arxiv.org/abs/1310.3973
Experiment design for biased models Most experiment design methods assume that the true system is in the model set. It is well known that the total error may be reduced by using simpler models, trading variance for bias. In the contribution below we study experiment design for such models.
D. Eckhard, H. Hjalmarsson, C.R. Rojas and M. Gevers Mean-squared error experiment design for linear regression models 16th IFAC Symposium on System Identification Brussels, Belgium, pp 1629-1634, 2012.
Experiment design for non-linear systems A graph theoretic approach is taken to optimal experiment design for non-linear systems in the contribution below.
P.E. Valenzuela, C.R. Rojas and H. Hjalmarsson Optimal input design for non-linear dynamic systems: a graph theory approach Proceedings 51st IEEE Conference on Decision and Control, Florence, Italy, 2013.
Parameter estimation in standard model structures, such as Box-Jenkins, can be seen as impulse response estimation with a rank constraint. By a convex relaxation of the constraint a convex problem can be obtained. In the contribution below, the nuclear norm is used as surrogate for the rank constraint.
H. Hjalmarsson, C.R. Rojas and J. Welsh Identification of Box-Jenkins models using structured {ARX} models and nuclear norm relaxation 16th IFAC Symposium on System Identification Brussels, Belgium, pp 322-327, 2012.
Sparse estimation l-1 methods such as LASSO depend on a regularization parameter which typically is selected using cross-validation. In the first contribution below, the statistical properties of the estimate are used to directly determine this parameter, leading to improved computational efficiency. In the second contribution, this technique is applied to sparse estimation of rational model structures.
C.R. Rojas and H. Hjalmarsson Sparse estimation based on a validation criterion Proceedings 50th IEEE Conference on Decision and Control Orlando, FA, USA, 2011
C.R. Rojas, B. Wahlberg and H. Hjalmarsson A Sparse Estimation Technique for General Model Structures European Control Conference, Zurich, Switzerland, 2013.
Variance analysis of block structured systems From a system identification perspective, understanding how where to place sensors in a block-structured system requires understanding of how sensors influence the accuracy of the estimate of a specific block. Below we report on results for cascaded systems.
N. Everitt, H. Hjalmarsson and C.R. Rojas A Geometric Approach to Variance Analysis of Cascaded Systems Proceedings 51st IEEE Conference on Decision and Control, Florence, Italy, 2013.