## Final Report Summary - LEARN (Limitations, Estimation, Adaptivity, Reinforcement and Networks in System Identification)

Publishable brief summary of the achievement of the project

This section should normally not exceed 1 page.

Stand alone description of the project and its outcomes

LEARN is a project that aims at developing more efficient tools for building mathematical models of dynamical systems from observed input-output data, so called System Identification. Significant results have been achieved in utilizing regularization in different forms. This has interesting links with machine learning and convexification. In a sense, a viable and useful alternative has been created to the conventional state-of-the-art methodology, which is based on a statistical framework of maximum likelihood methods. Regularization has also proven most useful to deal with structural issues, such as model orders, network structures and segmentation of models.

A model’s quality depend critically on the quality of available data and therefore the design of the experiment is the most important step in system identification. Unfortunately, the optimal experiment typically depends on the to be identified system. In the project, a general theoretical framework for adaptive experiment design of linear dynamical systems has been developed. Under quite general conditions, methods where the experiment design is updated continuously as the experiment progresses, using the latest available model as surrogate for the true system, inherit the

same asymptotic accuracy as when the experiment design is based on knowledge of the true system before-hand. This is indeed a practically very powerful result.

The main outcomes of theoretical and practical significance can be summarized as follows.:

1. The links to machine learning and Bayesian theory have been clearly established. A thorough analysis of the underlying mechanisms that determine the quality of a structured multi-input multi-output model has been provided. Advantages in performance over classical state-of the art methods have been clarified and useful software for the new methodologies have developed

2. Theoretical justification for on-line experiment design has been established and a framework for reliable computation of parameter estimates in multivariable dynamical models has been developed. Software based on the new findings has been developed and successfully tested.

3. Risk minimization has been introduced as an important tool for system identification and a new and most promising technique called Weighed Null Space Fitting has been developed.

This section should normally not exceed 1 page.

Stand alone description of the project and its outcomes

LEARN is a project that aims at developing more efficient tools for building mathematical models of dynamical systems from observed input-output data, so called System Identification. Significant results have been achieved in utilizing regularization in different forms. This has interesting links with machine learning and convexification. In a sense, a viable and useful alternative has been created to the conventional state-of-the-art methodology, which is based on a statistical framework of maximum likelihood methods. Regularization has also proven most useful to deal with structural issues, such as model orders, network structures and segmentation of models.

A model’s quality depend critically on the quality of available data and therefore the design of the experiment is the most important step in system identification. Unfortunately, the optimal experiment typically depends on the to be identified system. In the project, a general theoretical framework for adaptive experiment design of linear dynamical systems has been developed. Under quite general conditions, methods where the experiment design is updated continuously as the experiment progresses, using the latest available model as surrogate for the true system, inherit the

same asymptotic accuracy as when the experiment design is based on knowledge of the true system before-hand. This is indeed a practically very powerful result.

The main outcomes of theoretical and practical significance can be summarized as follows.:

1. The links to machine learning and Bayesian theory have been clearly established. A thorough analysis of the underlying mechanisms that determine the quality of a structured multi-input multi-output model has been provided. Advantages in performance over classical state-of the art methods have been clarified and useful software for the new methodologies have developed

2. Theoretical justification for on-line experiment design has been established and a framework for reliable computation of parameter estimates in multivariable dynamical models has been developed. Software based on the new findings has been developed and successfully tested.

3. Risk minimization has been introduced as an important tool for system identification and a new and most promising technique called Weighed Null Space Fitting has been developed.

## Kontakt

## Tematy

Information and communication technology applications - Network technologies - Physical sciences and engineering - Telecommunications**Numer rekordu**: 183360 /

**Ostatnia aktualizacja**: 2016-05-26

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