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Identification of Nonlinear Systems using Empirical Data and Prior Knowledge  An Optimization Approach
 Automatica
, 1996
"... The choice of a parametric model structure in empirical and semiempirical nonlinear modeling is usually viewed as an important and critical step. However, it is known that by augmenting the leastsquares identification criterion with a term that imposes penalty on the nonsmoothness of the model, ..."
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Cited by 16 (5 self)
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The choice of a parametric model structure in empirical and semiempirical nonlinear modeling is usually viewed as an important and critical step. However, it is known that by augmenting the leastsquares identification criterion with a term that imposes penalty on the nonsmoothness of the model, an optimal nonparametric model can be found explicitly. The optimal nonparametric model will depend on the particular form of the penalty, which can be looked upon as a priori knowledge, or the desired properties of the model. In this paper these results are extended in several directions, i) we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint, and how this influences the optimal model, ii) dynamic models and a general prediction error penalty are considered, iii) we present a practical numerical procedure for the identification of a close to optimal semiparametric model. The numerical approach is motivated by the...
SemiEmpirical Modeling of NonLinear Dynamic Systems through Identification of Operating Regimes and Local Models
 Neural Network Engineering in dynamic control systems
, 1995
"... . An offline algorithm for semiempirical modeling of nonlinear dynamic systems is presented. The model representation is based on the interpolation of a number of simple local models, where the validity of each local model is restricted to an operating regime, but where the local models yield a co ..."
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Cited by 7 (0 self)
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. An offline algorithm for semiempirical modeling of nonlinear dynamic systems is presented. The model representation is based on the interpolation of a number of simple local models, where the validity of each local model is restricted to an operating regime, but where the local models yield a complete global model when interpolated. The input to the algorithm is a sequence of empirical data and a set of candidate local model structures. The algorithm searches for an optimal decomposition into operating regimes, and local model structures. The method is illustrated using simulated and real data. The transparency of the resulting model and the flexibility with respect to incorporation of prior knowledge is discussed. 1 Introduction The problem of identifying a mathematical model of an unknown system from a sequence of empirical data is a fundamental one which arises in many branches of science and engineering. The complexity of solving such a problem depends on many factors, such as...
On Convergence Proofs in System Identification  A General Principle using ideas from Learning Theory
"... this paper are different from the ones used in (Ljung 1987). The present conditions may be more restrictive, particularly if we assume, as in Theorem 3, that z t belongs to a compact set. 4 Parameter and Structure Identification Parameterization of the model set is introduced in this section. The mo ..."
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Cited by 3 (0 self)
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this paper are different from the ones used in (Ljung 1987). The present conditions may be more restrictive, particularly if we assume, as in Theorem 3, that z t belongs to a compact set. 4 Parameter and Structure Identification Parameterization of the model set is introduced in this section. The model set is decomposed into structural and parametric levels, which allows structure identification to be studied in the same framework. Furthermore, we will show how the well known convergence result in (Ljung 1978) now follows directly. Let S be a set of model structures. A model structure S 2 S is a set of possibly nonlinear equations, which may be algebraic, difference, differential, or a combination. The equations may contain some unknown parameters `