Tensor-based system identification of large-scale 2D spatial-temporal systems
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.
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
Large-scale identification, Kronecker product, adaptive optics, multilinear optimization
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.
In this work, we handle both the identification of Vector AutoRegressive models with exogenous Inputs (VARX) and of state-space models when the coefficient-matrices are written as Kronecker products. Such models allow to predict the slopes (or wavefront) measurements in large-scale 2D arrays. Eventually we validate these methods on a dedicated optical setup.
B. Sinquin, M. Verhaegen, "“Identification of large-scale Kronecker Vector-AutoRegressive models”, IEEE Transactions on Automatic Control, under review, 2017.
B. Sinquin, M. Verhaegen, "“Large-scale identification of state-space models with Kronecker modeling”, IEEE Transactions on Automatic Control, under review, 2017.
G. Monchen, B. Sinquin, M. Verhaegen, "“Recursive Kronecker-based Vector Auto-Regressive identification for large-scale systems”, IEEE Control Systems Technology, under review, 2017.
B. Sinquin, M. Verhaegen, "“Subspace Identification of 1D Spatially-Varying Systems using Sequentially Semi-Separable matrices”, Proceedings of the American Control Conference, Boston, 2016.
B. Sinquin, M. Verhaegen, "“Towards scalable identification Towards Scalable Subspace Identification with Kronecker modeling”, Proceedings of the Benelux Meeting for Systems and Control, Spa, Belgium, 2017.
B. Sinquin, M. Verhaegen, "“Kronecker-ARX Models in Identifying (2D) Spatial-Temporal Systems”, Proceedings of IFAC, World Congress, Toulouse, France, 2017.
G. Monchen, "Recursive Kronecker-based Vector Auto-Regressive identification for large-scale Adaptive Optics systems", TU Delft, 2017.
P. Varnai, "Exploiting Kronecker structures, With applications to optimization problems arising in the field of adaptive optics", TU Delft, 2017.
M. Voorsluys, ''Subspace Identification of Roesser Models for large-scale adaptive optics", TU Delft, 2015.