Identification of structured state-space models

Chengpu Yu*, Lennart Ljung, Michel Verhaegen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

44 Citations (Scopus)


Identification of structured state-space (gray-box) model is popular for modeling physical and network systems. Due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for successful applications. In this paper, the non-convex gray-box identification problem is reformulated as a structured low-rank matrix factorization problem by exploiting the rank and structured properties of a block Hankel matrix constructed by the system impulse response. To address the low-rank optimization problem, it is first transformed into a difference-of-convex (DC) formulation and then solved using the sequentially convex relaxation method. Compared with the classical gray-box identification methods like the prediction-error method (PEM), the new approach turns out to be more robust against converging to non-global minima, as supported by a simulation study. The developed identification can either be directly used for gray-box identification or provide an initial parameter estimate for the PEM.

Original languageEnglish
Pages (from-to)54-61
Publication statusPublished - 2018


  • Difference-of-convex problem
  • Prediction-error method
  • Structured state-space model


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