A fast nonlinear model identification method

The identification of nonlinear dynamic systems using linear-in-the-parameters models is studied. A fast recursive algorithm (FRA) is proposed to select both the model structure and to estimate the model parameters. Unlike orthogonal least squares (OLS) method, FRA solves the least-squares problem recursively over the model order without requiring matrix decomposition. The computational complexity of both algorithms is analyzed, along with their numerical stability. The new method is shown to require much less computational effort and is also numerically more stable than OLS.

[1]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[2]  Jan C. WillemsInstitute.  The Computational Complexity of Decentralized Discrete-Event Control Problems , 1993 .

[3]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[4]  Kezhi Mao,et al.  Fast orthogonal forward selection algorithm for feature subset selection , 2002, IEEE Trans. Neural Networks.

[5]  W. Murray Wonham,et al.  Think Globally, Act Locally: Decentralized Supervisory Control , 1991, 1991 American Control Conference.

[6]  Carlo Drioli,et al.  Orthogonal least squares algorithm for the approximation of a map and its derivatives with a RBF network , 2000, Signal Process..

[7]  S. Billings,et al.  Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks , 1996 .

[8]  Stéphane Lafortune,et al.  Decentralized supervisory control: a new architecture with a dynamic decision fusion rule , 2002, Sixth International Workshop on Discrete Event Systems, 2002. Proceedings..

[9]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[10]  De-Shuang Huang,et al.  Determining the centers of radial basis probabilistic neural networks by recursive orthogonal least square algorithms , 2005, Appl. Math. Comput..

[11]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[12]  Steven I. Marcus,et al.  On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation , 1989, Math. Control. Signals Syst..

[13]  Heinz Unbehauen,et al.  Structure identification of nonlinear dynamic systems - A survey on input/output approaches , 1990, Autom..

[14]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[15]  S. Chen,et al.  Fast orthogonal least squares algorithm for efficient subset model selection , 1995, IEEE Trans. Signal Process..