LEARN  Project Funded by an Advanced Grant from the European
Research Council
The Project
LEARN is an acrynom for
Limitations, Estimation, Adaptivity, Reinforcement and Networks
in System Identification
It is a fiveyear 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 56, pp 449471.
The Principal Investigator is Lennart Ljung, LiU, and Håkan
Hjalmarsson, KTH, is coPI. The project is organized into five themes:
 Theme I: Encounters with Convex Programming Techniques
 A convex optimization problem has no local minima other than the
global one, and can be solved by efficient algorithms. It is
therefore very useful to formulate any task as a convex
problem.
 Theme II: Fundamental Limitations
 The CramerRao lower limit for variance of unbiased estimates represents
a fundamental limitation to what can be achieved by estimation and
identification. It is an important problem to fully investigate the
consequences of this.
 Theme III: Experiment Design and
Reinforcement Techniques
 Careful design of experiments may lead to essential improvement
of the model accuracy. At the same time it is important to
take the experinment cost (in a wide sense) into account.
 Theme IV: Potentials of Nonparametric
Models of Dynamical Systems
 The dominating approach in ``main stream'' system identification is to use parametric models and methods. An important reason for that is that control design methods are predominantly now model based and analytical. Also parametric models and methods have a strong statistical historical background ever since Gauss. The nonparametric approaches in system identification have mostly been confined to spectral analysis techniques for estimating frequency functions.
 Theme V: Managing Structural
Constraints
 The increasing use of physical modeling of integrated and complex systems in
e.g.the automotive, aerospace and process industry, results in highly
structured models.
Another source of motivation for this research theme stems from the many
emerging networked and decentralized engineering
applications, e.g. networked
control systems and wireless sensor networks.
Theme I: Encounters with Convex Programming Techniques
State of the art
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 kernellike 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 stateoftheart 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.
Objectives
The goal is to understand the potential of convexification and to
utilize modern convex programming techniques for system
identification problems. This may lead to more efficient
estimation algorithms, getting grips with the constant peril
of getting caught in local minima for greybox models and
nonlinear blackbox models. The links to machine learning
and Theme IV are also important to understand
Results
 Convexity Issues in System Identification.
 A survey of convexity issues in system identification was
presented as a plenary presentation at the ICCA conference in
Hangzhou in June 2013: The paper
and
the
slides.
 What can regularization offer for
estimation of dynamical systems?

A summary of the possibilties and usefulness of regularization in
system identification was presented in a plenary at ALCOSP
2013 in Caen, France: The paper and
the
slides.
Using fundamental system limitations to establish benchmarks
regarding what can be realistically achieved with given
resources is an often used concept in engineering.
The importance of understanding limitations in engineering systems imposed by
data based modeling is accentuated as complexity and structural
constraints grow. To this end the CramÃ©rRao lower bound (CRLB) is fundamental. It translates into performance bounds for model based
applications employing identified models, e.g. it implies a lower
bound on the regulatory precision in control applications.
While the basic expression for the CRLB is well known, understanding how it depends on system and model complexity as well as
experimental conditions during the data collection
has been subject to rather intense research for a range of problem
settings. Recently it has been recognized that
the variance of estimated frequency functions is subject to a
waterbed effect, reminiscent to Bode's sensitivity integral.
Results
Theme III: Experiment Design and
Reinforcement Techniques
State of the art
The limitations discussed in Theme II) above imply that it is impossible to
identify a complex system accurately with only a modest amount of
(noisy) sensor information. The key to circumvent this curse of
complexity is the observation that an application often requires only a
modest amount of system properties to be accurately
modelled.
Objectives
Thus carefully designed, but
still ``inexpensive'', experiments may provide sufficient information
for the intended application. Consider for example the very simple case of
optimizing the yield of a
product with respect to one parameter. The model of the yield can be
very poor far away from the optimum (as long as it does not predict
better yield than the real optimum); it is only close to the optimum
that the modeling accuracy becomes important. It is immediate from
this example that obtaining such models requires access to
actuation abilities: Measurements should
be concentrated to the vicinity of the optimal parameter value.
There are two wellknown issues that hamper the implementation of
this objective:
 (i) Computational restrictions:
 Many optimal
experiment design problems, e.g. those involving nonlinear dynamical
systems, correspond to highly nonconvex optimization problems.
 (ii) The
chicken and egg problem:
 Good experiments typically depend on the
to be identified system itself. In the example above, the optimum,
where the measurements should be taken, is
unknown.
Convexification has proved to be a viable route to cope with Issue i) for
linear dynamical systems.
Corresponding methods for nonlinear dynamical systems are still
lacking.
Results
Theme IV: Potentials of Nonparametric
Models of Dynamical Systems
State of the art
Various nonparametric methods have been important tools in statistics
since long. Nearest neighbour, kernel, and local
approximation techniques are successfully used to estimate
surfaces in regressor spaces. We
have ourselves experience in developing, analysing and
testing such local approaches (Direct Weight
Optimisation, DWO). Also Support Vector Machines, SVM,can
be understood as such kernel methods, although the formal
treatment is via parameter estimation. The convergence of
Machine Learning towards Statistical Learning (or the other
way around) has stressed the role of kernel
approximations. Gaussian Process regression
(originally conceived in the 1950's) for example has become
a widely used tool for function approximation in Machine
Learning also for applications to dynamical systems. Some very recent contributions, have shown that conventional parametric methods can be successfully combined with learning techniques even for estimating standard linear models.
The concept and use of manifold learning techniques is related
to this area. These are methods to identify areas (manifolds) in the
regressor space that are of special interest for a given
application. By focusing on the system's behaviour on that manifold,
simpler and more effective models can be constructed.
Objectives
The goal of the research in this area is to provide methodology and algorithms for estimating complex (nonlinear) dynamical systems in reliable and effective manners. We strongly feel that nonparametric methods are underutilised in the system identification research community and that powerful results can be obtained by adjoining manifold learning and machine learning strategies to conventional identification methods.
Results
 Encounters with System Identification:
 In the plenary at the 50th CDC/ECC in Orlando, the potentials of
Gaussian processes and Bayesian thinking for system identification
were outlined: The presentation, the paper
and
the video recording.
 On the estimation of transfer functions:

An extensive analysis of the use of Gaussian Processes techniques for
system identification has been presented in
Automatica
paper: T. Chen, H. Ohlsson and L. Ljung On the estimation of transfer functions,
regulariztions amd Gaussian processes 
Revisited
Automatica, Vol 48, pp 15251535,
2012.
Recently identifiability of systems composed of cascade,
feedforward, feedback and multiplicative
connections of linear dynamic and zero memory nonlinear elements have
been studied. In even more recent work it ha discussed how to
include structural information in subspace identification of ARMAX
models with unequal polynomial orders. It has been shown
quite surprisingly, there are certain configurations of
cascade systems where some of the sensors do not contribute with
information regarding system blocks further ``upstreams''.
Distributed signal processing very much targets the
emerging area of wireless sensor networks (WSN).
There is also a flood of results concerning
networked control but there exists few
results on identification of distributed and networked systems with
control as application.
The overall objective is to develop structure preserving
identification methods suitable for networked and decentralized
systems. This includes experiment design,
identification (e.g. subspace) and model reduction methods that
respect structural constraints.
It also includes design methods for
both communication strategies (between nodes) and sensor/actuator
placement in decentralized identification with the objective to
maximize modeling accuracy. This requires understanding how structural
information and decentralized data processing influence a model's
accuracy.
Results
Last modified: Sat Sep 7 08:38:40 CEST 2013