Identification of positive real models in subspace identification by using regularization
(2003) IEEE Transactions on Automatic Control — Vol. 48, n° 10, p. 1843-1847 (2003)
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- Abstract
- 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.
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Goethals, I., Van Gestel, T., Suykens, J., Van Dooren, P., & De Moor, B. (2003). Identification of positive real models in subspace identification by using regularization. IEEE Transactions on Automatic Control, 48(10), 1843-1847. https://doi.org/10.1109/TAC.203.817940 (Original work published 2003)