Parametrizations of linear dynamical systems: Canonical forms and identifiability

Glover, K.; Willems, J. L.

doi:10.1109/tac.1974.1100711

Cited by 254 publications

(103 citation statements)

References 10 publications

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“…28-29) is said to be locally identifiable. If this minimum is global, the structure is said to be globally identifiablesee [5,17,26] for a more detailed discussion.…”

Section: History Matching and Identifiabilitymentioning

confidence: 99%

Controllability, observability and identifiability in single-phase porous media flow

et al. 2008

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Over the past few years, more and more systems and control concepts have been applied in reservoir engineering, such as optimal control, Kalman filtering, and model reduction. The success of these applications is determined by the controllability, observability, and identifiability properties of the reservoir at hand. The first contribution of this paper is to analyze and interpret the controllability and observability of single-phase flow reservoir models and to investigate how these are affected by well locations, heterogeneity, and fluid properties. The second contribution of this paper is to show how to compute an upper bound on the number of identifiable parameters when history matching production data and to present a new method to regularize the history matching problem using a reservoir's controllability and observability properties. Keywords

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“…28-29) is said to be locally identifiable. If this minimum is global, the structure is said to be globally identifiablesee [5,17,26] for a more detailed discussion.…”

Section: History Matching and Identifiabilitymentioning

confidence: 99%

Controllability, observability and identifiability in single-phase porous media flow

et al. 2008

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“…19) We see that the process x1(t) and w(t) satisfy the same differential equation (in particular, the driving process is the same); by definition [see (5.10)], they also have the same initial condition. , where, however, the problem is treated in a deterministic context and no connection is made with signal model equivalence or with left invertibility.…”

Section: Proof Of Theorem 54mentioning

confidence: 97%

“…It is well known that if we extend SME by also allowing change of . basis in state space, then the resulting equivalence is the one that relates two systems if their corresponding spectral densities are equal (see [19]). …”

Section: Signal Model Equivalence (Sme)mentioning

confidence: 99%

A geometric approach to the singular filtering problem

Schumacher¹

1985

IEEE Trans. Automat. Contr.

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Abstract-We consider the least-squares filtering problem for a stationary Gaussian process when the observation is not fuJly corrupted by white noise, the so-called "singular" case. An optimal estimator is constructed consisting of an integrating part, which is, as in the regular case, computed from a spectral factorization or an equivalent matrix problem, and a differentiating part whose parameters are computed from a single matrix equation. This improves on older results which either work under restrictive assumptions, or describe the solution only as the result of some nested algorithm.

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“…structural forms are needed to cover the set of all systems [10], [45]. Glover and Willems [14] have argued that this is an avoidable problem; one can use "overlapping" or "pseudo-canonical" forms which have the advantage that each form can represent the majority of systems-typically, each form can represent "almost all" systems, in the measure-theoretic sense-but now each system can be represented in several such forms. Each system still has a unique representation in each form, however, which is all that matters for identification.…”

Section: Identifiable Parameterizationsmentioning

confidence: 99%

System identification using balanced parametrizations

Chou

Maciejowski

1997

IEEE Trans. Automat. Contr.

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Abstract-Some general issues in the "black-box" identification of multivariable systems are first discussed. It is then suggested that balanced parameterizations can be used to give identifiable forms. A particular advantage is that balanced parameterizations are known for several useful classes of linear dynamic models, including stable minimal models, minimum-phase models, positive-real models, and normalized coprime factor models. Before optimizing the parameters of balanced parameterizations, an initial model must be found. We use realization-based methods and so-called "subspace" methods for this purpose. These methods are very effective at finding accurate initial models without preliminary estimation of various structural indexes. The paper ends with two simulation examples, which compare the use of balanced parameterizations with more traditional ones, and three "real" examples based on practical problems: a distillation column, an industrial dryer, and the (irrational) spectrum of sea waves.

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Parametrizations of linear dynamical systems: Canonical forms and identifiability

Cited by 254 publications

References 10 publications

Controllability, observability and identifiability in single-phase porous media flow

Controllability, observability and identifiability in single-phase porous media flow

A geometric approach to the singular filtering problem

System identification using balanced parametrizations

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