Constrained subspace method for the identification of structured state-space models (cosmos)

Chengpu Yu, Lennart Ljung, Adrian Wills, Michel Verhaegen

Research output: Contribution to journalArticleScientificpeer-review

60 Citations (Scopus)
168 Downloads (Pure)


In this paper, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the systemparameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The non-convex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method (PEM) initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.
Original languageEnglish
Pages (from-to)4201-4214
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 2020

Bibliographical note

Accepted Author Manuscript


  • Subspace identification
  • Markov-parameter estimation
  • Hankel matrix factorization


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