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Perspectives on system identification
 In Plenary talk at the proceedings of the 17th IFAC World Congress, Seoul, South Korea
, 2008
"... System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous ne ..."
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Cited by 73 (2 self)
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System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications. System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric etc. At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods. A tutorial or a survey in a few pages is not quite possible. Instead, this presentation aims at giving an overview of the “science ” side, i.e. basic principles and results and at pointing to open problem areas in the practical, “art”, side of how to approach and solve a real problem. 1.
JustinTime Models with Applications to Dynamical Systems
 Dept. of EE, LinkOping University. S581 83 LinkOping
, 1997
"... System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatmen ..."
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Cited by 21 (3 self)
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System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatments of the estimation problem in statistics and system identification have mainly focused on global modeling approaches, i.e., the model has been optimized using the entire data set. However, when the number of samples becomes large, this approach becomes less attractive mainly because of the computational complexity. We instead assume that all observations are stored in a database, and that models are built dynamically as the actual need arises. When a model is really needed in a neighborhood around an operating point, a subset of the data closest to the operating point is retrieved from the database, and a local modeling operation is performed on that subset. For this concept, the name Jus...
Frequency Domain System Identification Toolbox
, 1994
"... Abstract: System identification often means the determination of linear models from inputoutput data. The behaviour of many systems can be described by an sdomain or zdomain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the ana ..."
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Cited by 14 (9 self)
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Abstract: System identification often means the determination of linear models from inputoutput data. The behaviour of many systems can be described by an sdomain or zdomain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the analysis of the residuals, that is, of the difference between the measured data and the model. However, even slight nonlinearities can be misleading, by causing part of the residuals nonexplicable by the linear model. We cannot simply tell if the excess residual error is due to undermodelling or to nonlinear system behaviour. This can lead to erroneous overmodelling. Therefore, characterisation of the nonlinear system behaviour is essential in the verification of linear models. The Frequency Domain System Identification Toolbox has been extended with analysis tools of nonlinear system behaviour. Specially designed excitation signals allow the description of nonlinearity levels. By this, model verification becomes possible even if nonlinear error terms excess linear additive noise. Copyright © 2006 IFAC
Some Results on Identifying Linear Systems Using Frequency Domain Data
 In Proc. 32nd IEEE Conference on Decision and Control
, 1993
"... The usefulness of frequency domain interpretations in linear systems is well known. In this contribution the connenctions between frequency domain and time domain expressions will be discussed. In particular, we consider some aspects of using frequency domain data as primary observations. 1 Introduc ..."
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Cited by 9 (1 self)
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The usefulness of frequency domain interpretations in linear systems is well known. In this contribution the connenctions between frequency domain and time domain expressions will be discussed. In particular, we consider some aspects of using frequency domain data as primary observations. 1 Introduction For linear systems the connections and interplay between timedomain and frequency domain aspects have proved to be most fruitful in all applications. We shall in this contribution discuss some aspects in applications to linear system identification. There are two sides of this interplay. One is to consider the primary observation to be in the timedomain, and then to interpret corresponding identification criteria, algorithms and properties in the frequency domain. There are many early results of this character, e.g. [9], [2], [1], [4]. More recently such results have been exploited and developed in [6]. The other side of the interplay is to consider the primary observations to be in th...
Frequency Domain Identification with Generalized Orthonormal Basis Functions
 IN PROC. 34TH IEEE CONFERENCE ON DECISION AND CONTROL
, 1995
"... A method is considered for identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain. To this end use is made of the empirical transfer function estimate (ETFE), identified from timedomain data. As a parametric model stru ..."
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Cited by 4 (1 self)
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A method is considered for identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain. To this end use is made of the empirical transfer function estimate (ETFE), identified from timedomain data. As a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions, being generalizations of the classical pulse, Laguerre and Kautz types of bases. An asymptotic analysis of the estimated models is provided and conditions for consistency are formulated. Explicit and transparent bias and variance expressions are established, the latter ones also valid in a situation of undermodelling.
Timedomain Identification of Dynamic Errorsinvariables Systems Using Periodic Excitation Signals
 In Submitted to IFAC Congress
, 1998
"... The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a nonparametric noise mo ..."
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Cited by 3 (1 self)
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The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a nonparametric noise model, estimated directly from the measured data, is used in a compensation strategy applicable to both least squares and total least squares estimation. The resulting least squares and total least squares methods are applicable in the errorsinvariables situation and give consistent estimates regardless of the noise. The feasibility of the idea is illustrated in a simulation study. Keywords: System identification; Least squares estimation; Errorsinvariables models. 1 Introduction One of the most important steps in the identification process is the experiment design. This involves, for example, deciding what signals to measure, choosing the sampling interval, and designing the excitation...
Applications Of Kautz Models In System Identification
 In Proceedings of the 12th IFAC World Congress
, 1993
"... . FIR, ARX or AR model structures can be used to describe many industrial processes. Simple linear regression techniques can be applied to estimate such models from experimental data. However, for low signal to noise ratios in combination with transfer function poles and noise model zeros close to t ..."
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Cited by 2 (0 self)
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. FIR, ARX or AR model structures can be used to describe many industrial processes. Simple linear regression techniques can be applied to estimate such models from experimental data. However, for low signal to noise ratios in combination with transfer function poles and noise model zeros close to the unit circle, a large number of model parameters are needed to generate adequate models. The Kautz model structure generalizes FIR, ARX and AR models. By using a priori knowledge about the dominating time constants and damping factors of the system, the model complexity is reduced, and the linear regression structure is retained. The objective of this contribution is to study an industrial example, where Kautz models have distinct advantages. The data investigated corresponds to aircraft flight flutter, which is a state when an aircraft component starts to oscillate. Key Words. Modeling, system identification, parameter estimation, aircraft modeling, Kautz functions. 1 INTRODUCTION To d...
Classical Model Validation for Control Design Purposes
 Mathematical Modelling of Systems
, 1995
"... Model Validation is at the heart of the System Identification process. Recently, much renewed interest has been expressed in so called "identification for control". This means that the design variables associated with the identification process are tailored to achieve models that are well suited for ..."
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Cited by 2 (0 self)
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Model Validation is at the heart of the System Identification process. Recently, much renewed interest has been expressed in so called "identification for control". This means that the design variables associated with the identification process are tailored to achieve models that are well suited for control design purposes. A separate, but closely related issue is to devise validation tests that give information about the model's quality and suitability for control design. This paper shows and discusses how a basic and classical residual test gives such information.  + Department of Electrical Engineering, Linkoping University, Linkoping, S58183, Sweden. Email: Ljung@isy.liu.se, Fax: (+46)13 282622. ++ Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, P.R.China. Email: Lguo@iss03.iss.ac.cn, Fax: (8610)2587343. 1 Introduction "Identification for Control" has since long been of m...
Identification of Volterra Kernels Using Interpolation
"... Abstract—This paper presents a new method for the identification of frequencydomain Volterra kernels. Since the nonlinear kernels often play a secondary role compared to the dominant, linear component of the system, it is worth establishing a balance between the degree of liberty of these component ..."
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Abstract—This paper presents a new method for the identification of frequencydomain Volterra kernels. Since the nonlinear kernels often play a secondary role compared to the dominant, linear component of the system, it is worth establishing a balance between the degree of liberty of these components and their effect on the overall accuracy of the model. This is necessary in order to reduce the model complexity, hence the required measurement length. Based on the assumption that frequencydomain kernels are locally smooth, the kernel surfaces can be approximated by interpolation techniques, thus reducing the complexity of the model. Similarly to the unreduced (Volterra) model, this smaller model is also i) linear in the unknowns; ii) only locally sensitive to its parameters; and iii) free of structural assumptions about the system. The parameter estimation boils down to solving a linear system of equations in the leastsquares (LS) sense. The design of the interpolation scheme is described and the performance of the approximation is analyzed and illustrated by simulation. The algorithm allows a significant saving in measurement time compared to other kernel estimation methods. Index Terms—Bspline, interpolation, nonlinear system, random multisine, system identification, Volterra kernel, Volterra series.
Efficient Construction of Transfer Functions from Frequency Response Data
 Dep. of EE, Linkoping University
, 1994
"... In this paper, we present a novel noniterative algorithm to identify linear timeinvariant systems from frequency response data. The algorithm is related to the recent timedomain subspace identification techniques. Promising results are obtained when the algorithm is applied to the real frequency ..."
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Cited by 1 (1 self)
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In this paper, we present a novel noniterative algorithm to identify linear timeinvariant systems from frequency response data. The algorithm is related to the recent timedomain subspace identification techniques. Promising results are obtained when the algorithm is applied to the real frequency data originating from a large flexible structure. A robustness analysis is performed and under weak conditions on the measurement noise, it is shown that the algorithm is consistent. 1 Introduction Recently, identification and control of large space structures has received considerable attention [18, 19, 20, 4, 14, 13]. This type of systems are also frequently encountered in the modal analysis area of mechanical engineering. Typically such systems are lightly damped and quite often as in the system analysis and control design of mechanical structures, high order models with many outputs are needed. For structural design purposes, the finite element method provides accurate enough models. Th...