Pseudo-canonical forms, identifiable parametrizations and simple parameter estimation for linear multivariable systems: Parameter estimation

Correa, Germán; Glover, K.

doi:10.1016/0005-1098(84)90102-x

Cited by 15 publications

(7 citation statements)

References 8 publications

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“…A pair (y( • ), u( • )) is said to be n-realizable =3~= (A, B, C) of order n, minimal, with rank (C) = p and Correa and Glover (1984 a) that if a pair (y( . ), u( • )) is n-realizable then 3 YEJf(n) such that (2.1) holds.…”

Section: Pco Input-output Modelsmentioning

confidence: 99%

“…In the case considered here this amounts to requiring that (y('), u( .» is n-realizable (linearity assumption and correct order choice), say, by~= (A, B, C), and that for the chosen parametrization P" (2.1) holds. Given the correct choice of order n, the requirement on the choice ofy eJ'(n) is equivalent to the nice row subset of the Hankel matrix of~indexed by y being linearly independent (Correa and Glover 1984 a).…”

Section: Parametrization Selection and IV Estimationmentioning

confidence: 99%

“…In a previous paper (Correa and Glover 1984 a) a set of parametrizations of multivariable linear input-output models (matrix-fraction descriptions or finitedifference equations) was introduced that exhibits three desirable properties for identification:…”

Section: Introductionmentioning

confidence: 99%

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Two-stage IV-based estimation and parametrization selection for linear multivariable identification

Correa

Glover

1987

International Journal of Control

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Previous work of the authors on the use of overlapping parametrizations of finitedifference equations in the identification of multivariable systems is continued. By considering numerical and accuracy issues, a two-stage, IV-based, joint parametrization-selection and parameter-estimation scheme is proposed. The parametrization selection seeks to ensure that the estimation problems are numerically well conditioned, whereas the second stage ensures statistical efficiency in certain circumstances.

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Section: Pco Input-output Modelsmentioning

confidence: 99%

Section: Parametrization Selection and IV Estimationmentioning

confidence: 99%

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Two-stage IV-based estimation and parametrization selection for linear multivariable identification

Correa

Glover

1987

International Journal of Control

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“…A large number of studies were carried out, mostly before the 90's, to define appropriate parametrisations of MIMO systems [see e.g. [11][12][13][14][15][16]. At this time, the authors pointed out that pseudo-canonical parametrisations are well-suited for a system identification.…”

Section: New Model Parametrisation Of Transfer Functionsmentioning

confidence: 99%

New developments for experimental modal analysis of aircraft structures

Vayssettes

Mercère

2015

MATEC Web of Conferences

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Abstract. This article presents an identification algorithm dedicated to the modal analysis of aircraft structures during flighttests. More specifically, this algorithm was designed to process short duration tests carried out with multi-input excitations. The identification problem is solved in the frequency domain and the limit effects are considered so as to avoid transient effects with short data sequences. To minimise the effects of the noise, a non-linear gradient-based optimisation method is used. Its performance is improved by the use of an appropriate over-parametrised matrix fraction descriptions. Because the cost function to be minimised is non-convex, this method is however sensitive to the initialisation. For this reason, an iterative instrumental variable method is used to find an initial estimate. This one gives a value of the cost-function sufficiently close to its global minimum so as to ensure a fast convergence of the optimisation. Thus, the algorithm presented in this article is a combination of two iterative methods that gives accurate mode estimations even with high level of noise, as shown on an illustrative example.

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“…Table 1 shows the structure specification, condition and results of Theorem 4.1, for a number of MFD forms: the canonical observability form [11]; the pseudo-canonical (overlapping) form [12], [13], [14]; the Hermite form [15], [16]; the diagonal form [17], [18] and the generalized pseudocanonical form [19]. …”

Section: ~)mentioning

confidence: 99%

Some asymptotic properties of multivariable models identified by equation error techniques

Hof

Janssen

1986

1986 25th IEEE Conference on Decision and Control

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Pseudo-canonical forms, identifiable parametrizations and simple parameter estimation for linear multivariable systems: Parameter estimation

Cited by 15 publications

References 8 publications

Two-stage IV-based estimation and parametrization selection for linear multivariable identification

Two-stage IV-based estimation and parametrization selection for linear multivariable identification

New developments for experimental modal analysis of aircraft structures

Some asymptotic properties of multivariable models identified by equation error techniques

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