| 1. |
- Lin, Weilu, et al.
(författare)
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On Consistency of Closed-Loop Subspace Identification with Innovation Estimation
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given, A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output simulation shows that itis consistent under closed-loop conditions, when traditional SIMs fail to provide consistent estimates.
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| 2. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Closed-Loop Subspace Identification with Innovation Estimation
- 2003
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Ingår i: Proceedings of the 13th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 9780080437095 ; , s. 887-892
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Konferensbidrag (refereegranskat)abstract
- Most subspace identication algorithms are not applicable to closed-loop identication because they require future input to be uncorrelated with pastinnovation. In this paper, we propose a new subspace identication method that remove this requirement by using a parsimonious model formulation with innovation estimation. A simulation example is included to show the effectiveness of the proposed method.
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| 3. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Comparison of Subspace Identification Methods for Systems Operating in Closed Loop
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress. - 9783902661753 ; , s. 82-82
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we analyze two recently proposed closed-loop subspace identification methods, referred to as innovation estimation method and whitening filter approach respectively. The similarity and difference between them are investigated in detail. It turns out that all closed-loop subspace identification methods can be classified as one-step, two-step, or multi-stage projection methods. A SISO closed-loop simulation shows that to identify a consistent model the whitening filter approach might require longer future and past horizons than the innovation estimation method.
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| 4. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
On Consistency of Closed-Loop Subspace Identification with Innovation Estimation
- 2004
-
Ingår i: Proceedings of the 43rd IEEE Conference on Decision and Control. - 0780386825 ; , s. 2195-2200
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given, A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output simulation shows that itis consistent under closed-loop conditions, when traditional SIMs fail to provide consistent estimates.
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| 5. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Parallel QR Implementation of Subspace Identification with Parsimonious Models
- 2003
-
Ingår i: Proceedings of the 13th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 9780080437095 ; , s. 1631-1636
-
Konferensbidrag (refereegranskat)abstract
- In this paper we reveal that the typical subspace identification algorithms use non-parsimonious model formulations, with extra terms in the model that appear to be non-causal. These terms are the causes for inflated variance in the estimates and partially responsible for the loss of closed-loop identifiability. We then propose a parallel parsimonious formulation of a new subspace identification algorithm and demonstrate the effectiveness of the proposed algorithm via simulation.
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| 6. |
- Qin, S. Joe, et al.
(författare)
-
A Novel Subspace Identification Approach with Enforced Causal Models
- 2007
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input-output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A,B,C,D) and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles.
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| 7. |
- Qin, S. Joe, et al.
(författare)
-
A Novel Subspace Identification Approach with Enforced Causal Models
- 2005
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 41:12, s. 2043-2053
-
Tidskriftsartikel (refereegranskat)abstract
- Subspace identification methods (SIMs) for estimating state-space models have been proven to be very useful and numerically efficient. They exist in several variants, but all have one feature in common: as a first step, a collection of high-order ARX models are estimated from vectorized input-output data. In order not to obtain biased estimates, this step must include future outputs. However, all but one of the submodels include non-causal input terms. The coefficients of them will be correctly estimated to zero as more data become available. They still include extra model parameters which give unnecessarily high variance, and also cause bias for closed-loop data. In this paper, a new model formulation is suggested that circumvents the problem. Within the framework, the system matrices (A,B,C,D) and Markov parameters can be estimated separately. It is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles.
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