Subspace identification of 1D spatially-varying systems using Sequentially Semi-Separable matrices

Baptiste Sinquin, Michel Verhaegen

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Abstract

We consider the problem of identifying 1D spatially-varying systems that exhibit no temporal dynamics. The spatial dynamics are modeled via a mixed-causal, anti-causal state space model. The methodology is developed for identifying the input-output map of e.g a 1D flexible beam described by the Euler-Bernoulli beam equation and equipped with a large number of actuators and sensors. It is shown that the static input-output map between the lifted inputs and outputs possess a so-called Sequentially Semi-Separable (SSS) matrix structure. This structure is of key importance to derive algorithms with linear computational complexity for controller synthesis of large-scale systems. A nuclear norm subspace identification method of the N2SID class is developed for estimating these state space models from input-output data. To enable the method to deal with a large number of repeated experiments a dedicated Alternating Direction Method of Multipliers (ADMM) algorithm is derived. It is shown in this paper that a nuclear norm relaxation on the SSS structure can be imposed which improves the estimates of the system matrices.
Original languageEnglish
Title of host publicationProceedings of the 2016 American Control Conference (ACC 2016)
EditorsK Johnson, G Chiu, D Abramovitch
Place of PublicationPiscataway, NY, USA
PublisherIEEE
Pages54-59
ISBN (Electronic)978-1-4673-8682-1
ISBN (Print)978-1-4673-8683-8
DOIs
Publication statusPublished - 2016
EventAmerican Control Conference (ACC), 2016 - Boston, MA, United States
Duration: 6 Jul 20168 Jul 2016

Conference

ConferenceAmerican Control Conference (ACC), 2016
Abbreviated titleACC 2016
CountryUnited States
CityBoston, MA
Period6/07/168/07/16

Keywords

  • nuclear norm subspace identification
  • spatially distributed systems
  • sequentially semi-separable matrices

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    Sinquin, B., & Verhaegen, M. (2016). Subspace identification of 1D spatially-varying systems using Sequentially Semi-Separable matrices. In K. Johnson, G. Chiu, & D. Abramovitch (Eds.), Proceedings of the 2016 American Control Conference (ACC 2016) (pp. 54-59). IEEE. https://doi.org/10.1109/ACC.2016.7524891