Identifiability of linear time-invariant differential-algebraic systems application of differential algebra

Ben-Zvi, Amos; McLellan, James A.; McAuley, Kimberley B.

doi:10.1109/cdc.2003.1272521

Cited by 2 publications

(7 citation statements)

References 7 publications

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“…One may test the identifi ability of System (19) using either a generalized Markov parameter approach (Ben-Zvi et al, 2003) or using a transfer-function based approach (Ben-Zvi et al, 2004). Using the transfer function based approach, we construct a vector S(p, s) whose entries are the independent coeffi cients from the transfer function C(p)[E(p)s+M(p)] -1 B(p) of the linearized system.…”

Section: P(t) > P Ref For All Time Inmentioning

confidence: 99%

Identifiability of Non-Linear Differential Algebraic Systems via a Linearization Approach

2008

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A system is identifi able if there exists a unique relationship between its input-output behaviour and the parameter values. Differential-Algebraic Equation (DAE) systems have an input-output behaviour that is described by a parameterized set of ordinary differential and algebraic equations. Methods proposed in the literature to test the identifi ability of DAE systems are based on the tools of differential algebra and rely on time-differentiation of model equations. As a result, even when dealing with a few states and parameters, the calculations required for these methods may become intractable. An alternative, which we propose, is to linearize the non-linear DAE system about some rest point and then test the identifi ability properties of the linearized system. In this work, we show that strong local identifi ability of the linearized DAE system provides a suffi cient condition for the strong local identifi ability of the original non-linear DAE system.Un système est identifi able s'il existe une relation unique entre son comportement entrée-sortie et les valeurs de paramètres. Les systèmes d'équations différentielles-algébriques (DAE) ont un comportement entrée-sortie qui est décrit par un ensemble paramétrisé d'équations différentielles et algébriques ordinaires. Les méthodes proposées dans la littérature scientifi que pour tester l'identifi abilité des systèmes DAE sont basées sur les outils de l'algèbre différentielle et reposent sur la différentiation en temps des équations de modèle. Ainsi, même lorsqu'il s'agit de quelques états et paramètres, les calculs requis pour ces méthodes peuvent devenir insolubles. Une autre façon de procéder, que nous proposons, consiste à linéariser le système DAE non linéaire vers un certain point de repos, puis de tester les propriétés d'identifi abilité du système linéarisé. Dans ce travail, nous montrons qu'une forte identifi abilité locale du système DAE linéarisé fournit une condition suffi sante pour la forte identifi abilité locale du système DAE non linéaire original.

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Section: P(t) > P Ref For All Time Inmentioning

confidence: 99%

Identifiability of Non-Linear Differential Algebraic Systems via a Linearization Approach

2008

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“…A linearization‐based approach has recently been proposed to test the identifiability of DAE systems by Ben‐Zvi et al (2004), with the aim of being able to treat larger‐scale systems. Herein, this linearization‐based approach is applied to a continuous‐reactor operation form of the PTC model originally proposed by Chen et al (1991).…”

Section: The Ptc Reaction Modelmentioning

confidence: 99%

“…As a result, attempting to eliminate all of the algebraic variables is generally unadvisable. One advantage of the test proposed by Ben‐Zvi et al (2004) is that this step is unnecessary.…”

Section: Solvability Of the Nonlinear Model Equationsmentioning

confidence: 99%

“…As summarized in Table 4, the nonlinear DAE system is first linearized and then the identifiability of the linearized system is assessed for identifiability. Details of how Steps 2 and 3 are achieved are available in Ben‐Zvi et al (2004).…”

Section: Identifiability Analysismentioning

confidence: 99%

“…3, C is given by Eq. 4, and Note that the subscript notation denotes partial differentiation, that is, The technique proposed by Ben‐Zvi et al (2004) requires that C ( p ) have full row rank and that B ( p ) have full column rank. This does not limit the generality of the test.…”

Section: Identifiability Analysismentioning

confidence: 99%

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Identifiability study of a liquid–liquid phase‐transfer catalyzed reaction system

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Identifiability of linear time-invariant differential-algebraic systems application of differential algebra

Cited by 2 publications

References 7 publications

Identifiability of Non-Linear Differential Algebraic Systems via a Linearization Approach

Identifiability of Non-Linear Differential Algebraic Systems via a Linearization Approach

Identifiability study of a liquid–liquid phase‐transfer catalyzed reaction system

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