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Abstract:This paper deals with the problem of piecewise auto regressive systems with exogenous input (PWARX) model identification based on clustering solution. This problem involves both the estimation of the parameters of the affine sub-models and the hyper planes defining the partitions of the state-input regression. The existing identification methods present three main drawbacks which limit its effectiveness. First, most of them may converge to local minima in the case of poor initializations because they are based on the optimization using nonlinear criteria. Second, they use simple and ineffective techniques to remove outliers. Third, most of them assume that the number of sub-models is known a priori. To overcome these drawbacks, we suggest the use of the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The results presented in this paper illustrate the performance of our methods in comparison with the existing approach. An application of the developed approach to an olive oil esterification reactor is also proposed in order to validate the simulation results.

We consider the clustering-based procedures for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. These methods exploit three main techniques which are clustering, linear identification, and pattern recognition. The clustering method based on thek-means algorithm is treated in this paper. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition while knowing the model ordersnaandnband the number of submodelss. The performance of this approach can be threatened by the presence of outliers and poor initializations. To overcome these problems, we propose new techniques for data classification. The proposed techniques exploit Chiu’s clustering technique and the self-artificial Kohonen neural network approach in order to improve the performance of both the clustering and the final linear regression procedure. Simulation results are presented to illustrate the performance of the proposed method.

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In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

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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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