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

Chengpu Yu, Lennart Ljung, Adrian Wills, Michel Verhaegen

Research output: Contribution to journalArticleScientificpeer-review


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
Number of pages13
JournalIEEE Transactions on Automatic Control
Publication statusE-pub ahead of print - 2020


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

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