Abstract
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.
Highlights
Hybrid systems have received great attention in the last years since the behavior of a broad class of physical systems interacts continuous and discrete-event phenomena
Several classes have been proposed in the literature for the representation of hybrid systems such as jump linear models (JL models) [1], Markov jump linear models (MJL models) [2], Mixed Logic Dynamical models (MLD models) [3, 4], Max-Min-Plus-Scaling systems (MMPS models) [5], Linear Complementarity models (LC models) [6], Extended Linear Complementarity models (ELC models) [7], and Piecewise Linear models (PWA models) [8, 9]
The properties of equivalence between PWARX models and other classes of hybrid systems allow transferring the results of piecewise affine (PWA) models to these classes [11]
Summary
Hybrid systems have received great attention in the last years since the behavior of a broad class of physical systems interacts continuous and discrete-event phenomena. The PWA models are considered in this paper These models are obtained by decomposing the state-input domain into a finite number of nonoverlapping convex polyhedral regions and by associating a simple linear or affine model to each region. This class of hybrid systems offers several interesting advantages. The analysis and control of PWA systems, like any other type of dynamic system, require a mathematical model of its behavior This model can be defined through a detailed analysis of the phenomena described by the system using the various laws that govern its operation. In the case of PWARX systems, the identification problem is known to be a challenging problem because it involves both
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