PWARX Model Identification Based on Clustering Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 163

PWARX Model Identification Based
on Clustering Approach

Zeineb Lassoued and Kamel Abderrahim

Abstract This chapter addresses the problem of clustering based procedure for the
identi

cation of PieceWise Auto-Regressive eXogenous (PWARX) models. In
order to overcome the main drawbacks of the existing methods such as their sen-
sitivity 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 Applica-

tions 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.

'

Keywords Identi cation PWARX systems Clustering approach Chiu ' s

algorithm DBSCAN algorithm Experimental validation

1 Introduction

Hybrid systems are heterogeneous dynamical systems that arise out of the inter-
action of continuous and discrete dynamics. The continuous behavior is the fact of
the natural evolution of the physical process whereas the discrete behavior can be
due to the presence of switches, operating phases, transitions, computer program
codes, etc. These hybrid dynamics characterize the behavior of a broad class of
physical systems, for example, the real-time control systems where physical pro-
cesses are controlled by embedded controllers. The notion of hybrid system can
also be used to represent complex nonlinear continuous systems. In fact, the
operating range of a nonlinear system can be decomposed into a group of operating