### 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 | United States |

City | Boston, MA |

Period | 6/07/16 → 8/07/16 |

### Keywords

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

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## Cite this

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