Larimore W. Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. 29 th IEEE Conference On Decision and Control, Honolulu, Hawaii, December 1990, pp. 596-604.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Overschee De Moor (1991a,1991b) The problem addressed in this paper is that of identifying a general state space model for combined deterministic stochastic systems directly from the input output data. Some papers in the past have already treated this problem but from a different viewpoint. In Larimore (1990) for instance, the problem is treated from a purely statistical point of view. There is no proof of correctness (in a sense of the algorithms being asymptotically unbiased) whatsoever. In De Moor et al. 1991) Verhaegen (1991) the problem is split up into two subproblems : deterministic ....

....through the complicated step 4 for the determination of B and D. This results in a simple and elegant algorithm with a slightly lower computational complexity as compared to algorithm 1. Another advantage of this simplified N4SID algorithm is that it is very closely related to existing algorithms (Larimore, 1990). This means that the analysis of this simplified algorithm can also be applied to the other algorithms, and can thus contribute to a better understanding of the mechanism of these algorithms. A disadvantage is that the results are not exact (unbiased) for finite i (except for special cases) but ....

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Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, 596-604.

....the range space of the extended observability matrix. Keywords. Consistency, subspace methods, identification, performance analysis, linear systems. 1. INTRODUCTION Subspace based methods for system identification have attracted a lot of interest in recent years (Van Overschee and De Moor, 1994; Larimore, 1990; Verhaegen, 1994; Viberg, 1995) These methods are easy to apply to identification of multivariable systems, and are based on solid numerical algorithms. The statistical properties are however not yet fully established. Initial work in this direction is e.g. reported in (Viberg et al. 1991; ....

....T n = 1 p N Y ff Pi U T ff : Here, S s is a diagonal matrix containing the n largest singular values and Q s contains the corresponding left singular vectors. 3. 2 IV 4SID The second type of estimators that will be analysed is here named IV 4SID (Van Overschee and De Moor, 1994; Larimore, 1990; Verhaegen, 1994) The reason for this name is that this approach is most easily explained in terms of instrumental variables (IV:s) A neat presentation of the topic can be found in (Viberg, 1995) Compared with Basic 4SID, the advantage with IV 4SID methods is that they can handle more general ....

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Larimore, W. E. (1990). Canonical Variate Analysis in Identification, Filtering and Adaptive Control. In: Proc. 29th CDC. Honolulu, Hawaii. pp. 596--604.

.... in (14) Without going into details here, it suffices to say that, by choosing appropriate weighting matrices W 1 and W 2 , all subspace algorithms for LTI systems can be interpreted in the above framework, including N4SID (Van Overschee and De Moor, 1994) MOESP (Verhaegen and Dewilde, 1992) CVA (Larimore, 1990), basic 4SID and IV 4SID (Viberg, 1994) It should be noted that for the basic 4SID algorithm condition (13) is not satisfied which implies that in general this method is not consistent. At this point, a clear distinction can be made between the algorithms that start from Gamma i to find the ....

....f . In what follows, we discuss the two classes of subspace identification algorithms mentioned above. The first class uses the state estimates e X i (the right singular vectors) to find the state space model. Algorithms that follow this approach are N4SID (Van Overschee and De Moor, 1994) and CVA (Larimore, 1990). The Acronym W 1 W 2 N4SID I li (Wp=U f ) y Wp CVA [ Y f =U f ) Wp=U f ) y : Y f =U f ) T ] Gamma1=2 (Wp=U f ) Gamma1=2 MOESP I li (Wp=U f ) y : Wp=U f ) Basic 4SID I li I j IV 4SID I li Phi Fig. 2. This table interprets different existing ....

Larimore, W.E. (1990). Canonical variate analysis in identification, filtering and adaptive control.

....which means that from all inputs and outputs the mean value was removed. 3 Subspace identification algorithms In this section the 3 algorithms that were used are shortly described. For more technical details we refer to a paper where the method was described. CVA Canonical variate analysis [3]. Constrained version of [4] N4SID Numerical algorithm for subspace state space system identification [5] The algorithm we used is the subid.m matlab function that comes with the previously cited book. MOESP SMI toolbox. The functions that have been used here are dordpo.m, dmodpo.m and ....

W.E. Larimore. Canonical variate analysis in identification, filtering and adaptive control. In Proc. 29th Conference on Decision and Control, pages 596--604, Hawai, 1990.

....rise to ill conditioned least squares problems. In [22] is was shown that a better (numerically more reliable) alternative to the above classical approach is via subspace model identification (SMI) This is also confirmed in the papers describing other, but related SMI algorithms, such as e.g. [12], 17] One variant of these SMI algorithms, namely the PI scheme, standing for the MOESP algorithm extended with instrumental variables based on past input data and developed in [23] also allows one to address to above identification problem in a consistent manner. Furthermore, this allows one ....

....when used properly, leads to a state space model with transition matrix F , such that F s quickly decay to zero. Such an explicit monitoring mechanism is simply not available when identifying marginally stable systems with the various originally developed SMI schemes, such as those in [21] [12] and [17] Stimulated by the very promissing results obtained in this paper, future research is proposed to consider more complex transformation of the shift operator, such as second order transformation which give rise to Kautz polynomials [2] and combinations of first and second order ....

LARIMORE, W., (1990), Canonical Variate Analysis in Identification, Filtering and Adaptive Control, In Proceedings of the 29th IEEE Conf. Decision and Control, 596--604, Hawaii.

....(which were first introduced by Jordan (1875) in linear algebra and then by Hotelling (1936) in the statistical community) have been used as a mathematical tool in the stochastic realization problem. In this paper we show how the approach by Akaike (1975) and others (e.g. Arun et al. 1990, Larimore, 1990) boils down to applying canonical correlation analysis to two matrices that are double infinite (i.e. have an infinite number of rows and columns) A careful analysis reveals the nature of this double infinity and we manage to reduce the canonical correlation approach to a semi infinite matrix ....

....of the system. 4 Orthogonal Projections In this section, we describe a new approach that avoids the formation of the covariance matrix (11) The identification scheme is based on geometrical insights and in contrast with previously described similar algorithms (Akaike (1975) Arun et al. 1990) Larimore (1990)) that needed double infinite block Hankel matrices, consistent estimates are obtained with semi infinite output block Hankel matrices. For sake of elegance of the proofs, covariance matrices will still be formed in the theoretical motivation that follows. The square root algorithm described in ....

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Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, 596-604.

....identification and frequency weighted balancing, the state space basis of the subspace identified models is shown to coincide with a frequency weighted balanced basis. 1 Introduction The identification problem considered in the combined deterministic stochastic subspace identification papers [4, 8, 10, 11] is the following : let u k 2 R m ; y k 2 R l be the observed input and output generated by the unknown system : x k 1 = Ax k Bu k w k ; y k = Cx k Du k v k ; 1) with E[ w k v k i w T l v T l j ] Q S S T R ffi kl 0 1 ; 2) and A; Q 2 R n Thetan ; B 2 R ....

....be observable respectively controllable. The main identification problem is then stated as : Given N input output measurements generated by the system (1) 2) find A; B; C; D;Q;R;S up to within a similarity transformation. Several solutions for this problem have been described in the literature [4, 8, 10, 11]. Although the solutions look very different at first sight, it was shown in [9] that these algorithms use the same basic subspace, but weighted in a different way. In this paper the effect of these weights will be further explored. It will be shown that the state space basis of the identified ....

Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, pp. 596-604.

....render it unbiased for all situations. Finally, it should be noted that by the choice of the weighting matrices W 1 and W 2 , other algorithms in the literature can be recuperated. Indeed, in (Van Overschee 1995) Van Overschee 1996a) it is described how the Canonical Variate Analysis by Larimore (Larimore 1990) and the MOESP algorithms by Verhaegen (Verhaegen 1994) can be retrieved by the appropriate choice of weighting matrices. 9 FREQUENCY DOMAIN EXTENSIONS In the problem statement at the beginning of this paper we started from input output measurements u k and y k (or just output measurements for ....

Larimore W.E. Canonical variate analysis in identification, filtering and adaptive control. Proc. 29th Conference on Decision and Control, Hawai, USA, pp. 596-604, 1990.

....The controller C(z) does not have to be explicitly given. 1 Introduction Subspace identification methods have been proven to be a valuable alternative for classical prediction error or instrumental variables methods [10, 13] Different breads of subspace identification methods have been published [8, 15, 20] of which a good overview is presented in [4, 18, 21] All of these subspace methods have a number of nice properties in common: unlike classical methods, they do not suffer from the problems caused by a priori parametrizations, initial estimates and non linear optimizations. They also identify ....

....closed loop data is thus a relevant topic. All of the published subspace identification methods however have one major drawback, they do not work when the data is gathered under closed loop experimental conditions as in Figure 1. Indeed, when there is feedback, the results of any of the algorithms [8, 15, 20] are asymptotically biased [11] This is also true for the Canonical Variate Analysis, despite the claim in the introduction of [9] In this paper we show how this problem can be solved, i.e. how subspace algorithms have to be modified in order to compute asymptotically unbiased results. For an ....

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Larimore W.E. Canonical variate analysis in identification, filtering and adaptive control. Proc. 29th Conference on Decision and Control, Hawai, USA, pp. 596-604, 1990.

....of this power spectrum. For disturbance modeling, the spectral factor of this power spectrum can then be used for instance in the design of an optimal disturbance rejection controller [5] For time domain measurements, a vast number of state space subspace identification algorithms is available [7, 11, 17, 18, 20, 21]. One of the advantages of these algorithms over the classical prediction error methods [14] is that there is no need for an explicit parametrization, which is typically needed to start up the prediction error algorithms. With subspace identification algorithms the only parameter needed is the ....

Larimore W.E. Canonical variate analysis in identification, filtering and adaptive control. Proc. 29th Conference on Decision and Control, Hawai, USA, pp. 596-604, 1990.

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Larimore W. Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. 29 th IEEE Conference On Decision and Control, Honolulu, Hawaii, December 1990, pp. 596-604.

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W. LARIMORE, Canonical variate analysis in identification, filtering and adaptive control, in Proceedings of the 29th IEEE Conference on Decision and Control, Hawaii, 1990, pp. 596--604.

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Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, pp 596-604.

No context found.

Larimore W. Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. 29 th IEEE Conference On Decision and Control, Honolulu, Hawaii, December 1990, pp. 596-604.

No context found.

Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, pp. 596-604.

No context found.

Larimore W. Canonical variate analysis in identification, filtering and adaptive control. Proc. 29th Conference on Decision and Control, Hawai, December 1990, pp.596-604.

No context found.

Larimore W.E. Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, December 1990.

No context found.

W. LARIMORE, Canonical variate analysis in identification, filtering and adaptive control, in Proceedings of the 29th IEEE Conference on Decision and Control, Hawaii, 1990, pp. 596--604.

No context found.

Larimore W.E. (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proceedings of the 29th Conference on Decision and Control, Hawaii, pp 596-604.

No context found.

W.E. Larimore (1990). Canonical Variate Analysis in Identification, Filtering, and Adaptive Control. Proc. 29th IEEE Conference on Decision and Control, pp. 596--604.

No context found.

Larimore, W., (1990), Canonical Variate Analysis in Identification, Filtering and Adaptive Control, In Proceedings of the 29th IEEE Conf. Decision and Control, 596--604, Hawaii.

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