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1.
  • Gerdin, Markus, et al. (creator_code:aut_t)
  • Global Identifiability of Complex Models, Constructed from Simple Submodels
  • 2007
  • record:In_t: Modeling, Estimation and Control. - Linköping : Linköping University Electronic Press. - 9783540735694 ; , s. 123-133
  • swepub:Mat_report_t (swepub:level_scientificother_t)abstract
    • It is a typical situation in modern modeling that a total model is built up from simpler submodels, or modules, for example residing in a model library. The total model could be quite complex, while the modules are well understood and analysed. A procedure to decide global parameter identifiability for such a collection of model equations of differential-algebraic nature is suggested. It is shown how to make use of the natural modularization of the model structure. Basically, global identifiability is obtained if and only if each module is identifiable, and the connecting signals can be retrieved from the external signals, without knowledge of the values of the parameters.
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2.
  • Gerdin, Markus, 1977-, et al. (creator_code:aut_t)
  • On Parameter and State Estimation for Linear Differential-Algebraic Equations
  • 2007
  • record:In_t: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 43:3, s. 416-425
  • swepub:Mat_article_t (swepub:level_refereed_t)abstract
    • The current demand for more complex models has initiated a shift away from state-space models towards models described by differential-algebraic equations (DAEs). These models arise as the natural product of object-oriented modeling languages, such as Modelica. However, the mathematics of DAEs is somewhat more involved than the standard state-space theory. The aim of this work is to present a well-posed description of a linear stochastic differential-algebraic equation and more importantly explain how well-posed estimation problems can be formed. We will consider both the system identification problem and the state estimation problem. Besides providing the necessary theory we will also explain how the procedures can be implemented by means of efficient numerical methods.
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3.
  • Gerdin, Markus, 1977-, et al. (creator_code:aut_t)
  • Parameter Estimation in Linear Differential-Algebraic Equations
  • 2003
  • record:In_t: Proceedings of the 13th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 9780080437095 ; , s. 1530-
  • swepub:Mat_conferencepaper_t (swepub:level_refereed_t)abstract
    • This report describes how parameter estimation can be performed in linear DAE systems. Both time domain and frequency domain identification are examined. The results are exemplified on a small system. A potential application for the algorithms is to make parameter estimation in models generated by a modeling language like Modelica.
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4.
  • Gerdin, Markus, 1977-, et al. (creator_code:aut_t)
  • Well-Posedness of Filtering Problems for Stochastic Linear DAE Models
  • 2005
  • record:In_t: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 350-355
  • swepub:Mat_conferencepaper_t (swepub:level_refereed_t)abstract
    • Modern modeling tools often give descriptor or DAE models, i.e., models consisting of a mixture of differential and algebraic relationships. The introduction of stochastic signals into such models in connection with filtering problems raises several questions of well-posedness. The main problem is that the system equations may contain hidden relationships affecting variables defined as white noise. The result might be that certain physical variables get infinite variance or contain formal differentiations of white noise. The paper gives conditions for well-posedness in terms of certain subspaces defined by the system matrices.
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5.
  • Gerdin, Markus, 1977- (creator_code:aut_t)
  • Identification and Estimation for Models Described by Differential-Algebraic Equations
  • 2006
  • swepub:Mat_doctoralthesis_t (swepub:level_scientificother_t)abstract
    • Differential-algebraic equations (DAEs) form the natural way in which models of physical systems are delivered from an object-oriented modeling tool like Modelica. Differential-algebraic equations are also known as descriptor systems, singular systems, and implicit systems. If some constant parameters in such models are unknown, one might need to estimate them from measured data from the modeled system. This is a form of system identification called gray box identification. It may also be of interest to estimate the value of time-varying variables in the model. This is often referred to as state estimation. The objective of this work is to examine how gray box identification and estimation of time-varying variables can be performed for models described by differential-algebraic equations.If a model has external stimuli that are not measured or uncertain measurements, it is often appropriate to model this as stochastic processes. This is called noise modeling. Noise modeling is an important part of system identification and state estimation, so we examine how well-posedness of noise models for differential-algebraic equations can be characterized. For well-posed models, we then discuss how particle filters can be implemented for estimation of time-varying variables. We also discuss how constant parameters can be estimated.When estimating time-varying variables, it is of interest to examine if the problem is observable, that is, if it has a unique solution. The corresponding property when estimating constant parameters is identifiability. In this thesis, we discuss how observability and identifiability can be determined for DAEs. We propose three approaches, where one can be seen as an extension of standard methods for state-space systems based on rank tests.For linear DAEs, a more detailed analysis is performed. We use some well-known canonical forms to examine well-posedness of noise models and to implement estimation of time-varying variables and constant parameters. This includes formulation of Kalman filters for linear DAE models. To be able to implement the suggested methods, we show how the canonical forms can be computed using numerical software from the linear algebra package LAPACK.
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