Identification of dynamic systems using Piecewise-Affine basis function models

Wen, Chengtao; Wang, Shuning; Jin, Xin; Ma, Xiaoyan

doi:10.1016/j.automatica.2007.03.003

Cited by 48 publications

(30 citation statements)

References 20 publications

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“…This procedure is also applied in [27] for another CPWL model. Using similar definitions, one can get the "derivative" to establish gradient-based method for (5).…”

Section: Estimation Algorithmmentioning

confidence: 98%

“…[9], a series of CPWL models, hinging hyperplanes, high-level canonical piecewise linear representation, generalized hinging hyperplanes are given by [1,15,26], respectively. Some identification algorithms are proposed, such as [11,17,18,27,28]. Along with this progress, CPWL functions have been wildly analyzed and applied for control and optimization, see [4,6,14,25,29] and etc.…”

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confidence: 99%

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Parameters estimation of hinging hyperplanes using median squared error criterion

Huang

Wang

2011

Int. J. Control Autom. Syst.

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This paper considers parameter estimation for nonlinear model using median squared error (MSE) criterion, which is limited to linear model in the past. It is shown that applying MSE, the essence of estimating parameters for hinging hyperplanes (HH) and linear model are the same. Motivated by this fact, MSE estimation is discussed for HH. A local optimality condition is given and based on this condition, an algorithm using linear programming technique is proposed. Numerical experiments show the good performance of the proposed estimation strategy and algorithm.

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“…This procedure is also applied in [27] for another CPWL model. Using similar definitions, one can get the "derivative" to establish gradient-based method for (5).…”

Section: Estimation Algorithmmentioning

confidence: 98%

mentioning

confidence: 99%

Parameters estimation of hinging hyperplanes using median squared error criterion

Huang

Wang

2011

Int. J. Control Autom. Syst.

Self Cite

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“…This problem consists in building mathematical models of hybrid systems from observed input-output data. The PWARX models have attracted a considerable attention in recent years, since they provide an efficient solution for modeling a wide range of engineering applications (Roll et al 2004;Nakada et al 2005;Wen et al 2007;Xu et al 2012). In addition, these models are able to approximate any nonlinear system with arbitrary accuracy (Lin and Unbehauen 1992).…”

Section: Introductionmentioning

confidence: 99%

PWARX Model Identification Based on Clustering Approach

Lassoued

Abderrahim

2014

Complex System Modelling and Control Through Intelligent Soft Computations

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This chapter addresses the problem of clustering based procedure for the identification of PieceWise Auto-Regressive eXogenous (PWARX) models. In order to overcome the main drawbacks of the existing methods such as their sensitivity to poor initializations and the existence of outliers, we propose the use of the Chiu's clustering algorithm and the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. A comparative study of the two proposed approaches with the k-means method is achieved in simulation. The results of experimental validation are also presented to illustrate the effectiveness of the proposed methods.

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“…(Nonlinear system identification) The following system, firstly proposed by Narendra and Parthasarathy (1990) for neural networks identification, is considered a benchmark for black-box identification technique evaluation (Verdult et al, 2002;Nie, 1994;Boukhris et al, 1999;Wen et al, 2007):…”

Section: Examplementioning

confidence: 99%

Nonlinear system identification using heterogeneous multiple models

Orjuela¹,

Marx²,

Ragot³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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Multiple models are recognised by their abilities to accurately describe nonlinear dynamic behaviours of a wide variety of nonlinear systems with a tractable model in control engineering problems. Multiple models are built by the interpolation of a set of submodels according to a particular aggregation mechanism, with the heterogeneous multiple model being of particular interest. This multiple model is characterized by the use of heterogeneous submodels in the sense that their state spaces are not the same and consequently they can be of various dimensions. Thanks to this feature, the complexity of the submodels can be well adapted to that of the nonlinear system introducing flexibility and generality in the modelling stage. This paper deals with off-line identification of nonlinear systems based on heterogeneous multiple models. Three optimisation criteria (global, local and combined) are investigated to obtain the submodel parameters according to the expected modelling performances. Particular attention is paid to the potential problems encountered in the identification procedure with a special focus on an undesirable phenomenon called the no output tracking effect. The origin of this difficulty is explained and an effective solution is suggested to overcome this problem in the identification task. The abilities of the model are finally illustrated via relevant identification examples showing the effectiveness of the proposed methods.

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Identification of dynamic systems using Piecewise-Affine basis function models

Cited by 48 publications

References 20 publications

Parameters estimation of hinging hyperplanes using median squared error criterion

Parameters estimation of hinging hyperplanes using median squared error criterion

PWARX Model Identification Based on Clustering Approach

Nonlinear system identification using heterogeneous multiple models

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