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 language | English |
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Title of host publication | Proceedings of the 2016 American Control Conference (ACC 2016) |
Editors | K Johnson, G Chiu, D Abramovitch |
Place of Publication | Piscataway, NY, USA |
Publisher | IEEE |
Pages | 54-59 |
ISBN (Electronic) | 978-1-4673-8682-1 |
ISBN (Print) | 978-1-4673-8683-8 |
DOIs | |
Publication status | Published - 2016 |
Event | American Control Conference (ACC), 2016 - Boston, MA, United States Duration: 6 Jul 2016 → 8 Jul 2016 |
Conference
Conference | American Control Conference (ACC), 2016 |
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Abbreviated title | ACC 2016 |
Country/Territory | United States |
City | Boston, MA |
Period | 6/07/16 → 8/07/16 |
Bibliographical note
Accepted Author ManuscriptKeywords
- nuclear norm subspace identification
- spatially distributed systems
- sequentially semi-separable matrices