Tensor-based system identification of large-scale 2D spatial-temporal systems

Background

The identification of multi-dimensional systems with a large number of input-output data cannot be handled with classical methods, whether the model structure is VARX or state-space. For a 2D network with NxN nodes with N large, the spatial coupling between the neighbours prevents from handling each node separately. Examples of applications for such spatial-temporal systems are numerous in control for high resolution imaging, e.g adaptive optics for large-scale telescopes.

Goal/ objective

The challenge lies in deriving algorithms that are, on the one hand, scalable in terms of data storage as well as in terms of computational complexity in identifying and using models in subsequent control design, and on the other hand, that still ensures similar prediction performances compared to the unstructured least-squares estimates. Reshaping the sensor and actuator data that are sampled on a 2D grid into a  tensor of pre-determined size enables to exhibit low-rank structures that allow high data compression and efficient identification algorithms.

In 2D networks, matrices present a two-level structure that is efficiently represented using the Kronecker product. The spatial dynamics are contained in the global matrices which are written as a finite sum of a Kronecker products between low dimensional matrices.

Project team members

• Baptiste Sinquin
• prof. Michel Verhaegen

Keywords

Large-scale identification, Kronecker product, adaptive optics, multilinear optimization

Sponsored by

This research is part of the iCON project which is sponsored by the Advanced Grant Program of the European Research Council. This funding will bring a core team of 6 temporary researchers together with world wide leading experts for a period of 5 years which started early 2014.