Learning Dynamical Systems

Learning dynamical systems is an area closely related to machine learning, cyber-physical systems as well as real-time big data analytics, and it provides backbone algorithms for digitalization of industry and society. Among others, it is core technology in autonomous systems with applications such as smart buildings, self-driving vehicles, and self-learning robots. In this project we focus on three key themes: Fundamental techniques concerns learning parsimonious models in a statistical and computationally efficient way. Active and on-line learning concaperns how to improve data-efficiency by actively controlling the excitation of the system in a sequential manner. Dynamical networked systems addresses issues of relevance to learning of interconnected dynamical systems, a field rapidly increasing in importance thanks to the fast development of 5g communication technology and the Internet-Of-Things paradigm.

More specifically, in a first step in this project we will consider the extension of Weighted Null-Space Fitting (WNSF) to rational non-linear models. WNSF is a novel multi-step least-squares algorithm for identification of multi-input multi-output (MIMO) linear black-box models which has proven to be highly competitive with state-of-the art methods such as the Prediction Error Method and Subspace identification. The possibility to handle MIMO models makes this very interesting and rational models are common in several domains, e.g.reaction networks. The plan is to subsequently extend the family of models to rational polynomial models by way of rank constraints and rank relaxations such as for example nuclear and atomic norms. It will also be investigated if this approach can be combined with the Simulated Prediction Error Method (SPEM), which is a method for estimation of models where there is no simple one-to-one correspondence between observations and driving noise/disturbances. SPEM is currently under development at the department and the combination of the two approaches could potentially lead to a breakthrough for estimation of non-linear models.

Project team

Project funding and duration

This project is funded by WASP, Wallenberg AI, Autonomous Systems and Software Program, with duration 2017-09–2021-09.

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Håkan Hjalmarsson
Professor of Signal Processing

My research interests cover system identification, process modeling and control, and communication network