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<p>This paper studies the recursive identification problem of the state space model in the framework of the subspace method in closed-loop. Based on the constrained least squares and the innovation estimation method, a recursive closed-loop subspace identification method with prior information is proposed. The key to this method is to avoid the calculation burden, such as singular value decomposition, or <i>QR</i> decomposition in offline identification, and to circumvent the influence of the past innovation on the future input in the closed-loop feedback controller. The constrained least squares method constructs a linear regression problem and the Hankel matrix of the impulse response parameters is obtained by Kung’s realization algorithm, which avoids the recursive update of the extended observability matrix or state variable sequences. An unbiased estimate of the noise term can be given by the innovation estimation method, which solves the correlation problem of the past noise and the future input. The effectiveness of the proposed identification method is illustrated by the simulation studies.</p>

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Recursive Closed-Loop Subspace Identification with Prior Information using the Constrained Least Squares

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Miao Yu,
  • Bowen Yang,
  • Ge Guo,
  • Jianchang Liu

摘要

This paper studies the recursive identification problem of the state space model in the framework of the subspace method in closed-loop. Based on the constrained least squares and the innovation estimation method, a recursive closed-loop subspace identification method with prior information is proposed. The key to this method is to avoid the calculation burden, such as singular value decomposition, or QR decomposition in offline identification, and to circumvent the influence of the past innovation on the future input in the closed-loop feedback controller. The constrained least squares method constructs a linear regression problem and the Hankel matrix of the impulse response parameters is obtained by Kung’s realization algorithm, which avoids the recursive update of the extended observability matrix or state variable sequences. An unbiased estimate of the noise term can be given by the innovation estimation method, which solves the correlation problem of the past noise and the future input. The effectiveness of the proposed identification method is illustrated by the simulation studies.