Identification of positive real models in subspace identification by using regularization
In time-domain subspace methods for identifying linear-time invariant dynamical systems, the model matrices are typically estimated from least squares, based on estimated Kalman filter state sequences and the observed outputs and/or inputs. It is well known that for an infinite amount of data, this...
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| Veröffentlicht in: | IEEE transactions on automatic control 2003-10, Vol.48 (10), p.1843-1847 |
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| container_title | IEEE transactions on automatic control |
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| creator | Goethals, I. Van Gestel, T. Suykens, J. Van Dooren, P. De Moor, B. |
| description | In time-domain subspace methods for identifying linear-time invariant dynamical systems, the model matrices are typically estimated from least squares, based on estimated Kalman filter state sequences and the observed outputs and/or inputs. It is well known that for an infinite amount of data, this least squares estimate of the system matrices is unbiased, when the system order is correctly estimated. However, for a finite amount of data, the obtained model may not be positive real, in which case the algorithm is not able to identify a valid stochastic model. In this note, positive realness is imposed by adding a regularization term to a least squares cost function in the subspace identification algorithm. The regularization term is the trace of a matrix which involves the dynamic system matrix and the output matrix. |
| doi_str_mv | 10.1109/TAC.2003.817940 |
| format | Article |
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| subjects | Algorithms Applied sciences Collaborative work Computer science control theory systems Control theory. Systems Cost function Councils Covariance matrix Dynamical systems Dynamics Exact sciences and technology Least squares approximation Least squares method Least squares methods Mathematical analysis Matrices Miscellaneous Modelling and identification Regularization State estimation Stochastic processes Stochastic systems Subspaces Time domain analysis |
| title | Identification of positive real models in subspace identification by using regularization |
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