| 1. |
- Akçay, Hüseyin, et al.
(författare)
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On the Choice of Norms in System Identification
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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| 2. |
- Akçay, Hüseyin, et al.
(författare)
-
The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the lest-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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| 3. |
- Akçay, Hüseyin, et al.
(författare)
-
The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
- 1994
-
Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; 23:5, s. 329-338
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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| 4. |
- Bencherki, Fethi, et al.
(författare)
-
Basis transform in linear switched system models from input–output data
- 2023
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Ingår i: International Journal of Adaptive Control and Signal Processing. - 0890-6327.
-
Tidskriftsartikel (refereegranskat)abstract
- This article addresses the problem of basis correction in the context of linear switched-system (LSS) identification from input–output data. It is often the case that identification algorithms for the LSSs from input–output data operate locally. The local submodel estimates, identified individually by subspace algorithms from the input-output data, reside in different-state bases, which mandates performing a basis correction that facilitates their coherent patching for the ultimate goal of performing output predictions for arbitrary inputs and switching sequences. We formulate a persistence of excitation condition for the inputs and the switching sequences that guarantees the presented approach’s success. These conditions are mild in nature,which proves the practicality of the devised algorithm. We supplement the theoretical findings with an elaborating numerical simulation example.
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| 5. |
- Bencherki, Fethi, et al.
(författare)
-
Realization of multi-input/multi-output switched linear systems from Markov parameters
- 2023
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Ingår i: Nonlinear Analysis: Hybrid Systems. - : Elsevier BV. - 1751-570X. ; 48
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the discrete states have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, stationary point set of a Hankel matrix with fixed dimensions built from the Markov parameters is examined. Splitting of this set into disjoint intervals and complements reveals linear time-invariant dynamics prevailing on these intervals. Clustering over a feature space permits recovery of the discrete states up to similarity transformations which is complete if a unimodality assumption holds and the discrete states satisfy a residence requirement. In the third stage, the switching sequence is estimated by three schemes. The first scheme is non-iterative in time. The second scheme is based on matching the estimated and the true Markov parameters of the SLS system over segments. The third scheme works also on the same principle, but it is a discrete optimization/hypothesis testing algorithm. The three schemes operate on different dwell time and model structure requirements, but the dwell time requirements are weaker than that needed to recover the discrete states. In the fourth stage, the discrete state estimates are brought to a common basis by a novel basis transformation which is necessary for predicting outputs to prescribed inputs. Robustness of the four-stage algorithm to amplitude bounded noise is studied and it is shown that small perturbations may only produce small deviations in the estimates vanishing as noise amplitude diminishes. Time complexities of the stages are also studied. A numerical example illustrates the derived results.
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| 6. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Subspace-based Identification of Infinite-dimensional Multivariable Systems from Frequency-response Data
- 1996
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 32:6, s. 885-902
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Tidskriftsartikel (refereegranskat)abstract
- A new identification algorithm which identifies low complexity models of infinite-dimensional systems from equidistant frequency-response data is presented. The new algorithm is a combination of the Fourier transform technique with the recent subspace techniques. Given noisefree data, finite-dimensional systems are exactly retrieved by the algorithm. When noise is present, it is shown that identified models strongly converge to the balanced truncation of the identified system if the measurement errors are covariance bounded. Several conditions are derived on consistency, illustrating the trade-offs in the selection of certain parameters of the algorithm. Two examples are presented which clearly illustrate the good performance of the algorithm.
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| 7. |
- McKelvey, Tomas, et al.
(författare)
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An Efficient Frequency Domain State-Space Identification Algorithm : Robustness and Stochastic Analyis
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 3348-3353 vol.4
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present and analyze a novel algorithm for identifying linear time-invariant discrete time state-space models from frequency response data. The algorithm is noniterative and exactly recovers a true system of order n, if n+2 noise-free uniformly spaced frequency response measurements are given. Analysis show that if the measurements are perturbed with errors upper bounded by ε the identification error will be upper bounded by ε and hence the algorithm is robust. An asymptotic stochastic analysis show, under weak assumptions, that the algorithm is consistent if the measurements are contaminated with noise.
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| 8. |
- McKelvey, Tomas, et al.
(författare)
-
An Efficient Frequency Domain State-Space Identification Algorithm
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 3359-3364 vol.4
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present and analyze a novel algorithm for identifying linear time-invariant discrete time state-space models from frequency response data. The algorithm is noniterative and exactly recovers a true system of order n, if n+2 noise-free uniformly spaced frequency response measurements are given. Analysis show that if the measurements are perturbed with errors upper bounded by ε the identification error will be upper bounded by ε and hence the algorithm is robust. An asymptotic stochastic analysis show, under weak assumptions, that the algorithm is consistent if the measurements are contaminated with noise.
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| 9. |
- McKelvey, Tomas, 1966-, et al.
(författare)
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Efficient Construction of Transfer Functions from Frequency Response Data
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we present a novel non-iterative algorithm to identify linear time-invariant systems from frequency response data. The algorithm is related to the recent time-domain subspace identification techniques. Promising results are obtained when the algorithm is applied to the real frequency data originating from a large flexible structure. A robustness analysis is performed and under weak conditions on the measurement noise, it is shown that the algorithm is consistent.
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| 10. |
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