Abstract
Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors. Since a general method for the analysis of hybrid systems is not available, some researchers have focused on specific types of hybrid systems. Piecewise affine (PWA) systems are one of the subsets of hybrid systems. The identification of PWA systems includes the estimation of the parameters of affine subsystems and the coefficients of the hyperplanes defining the partition of the state-input domain. In this paper, we have proposed a PWA identification approach based on a modified clustering technique. By using a fuzzy PCA-guided robust k-means clustering algorithm along with neighborhood outlier detection, the two main drawbacks of the well-known clustering algorithms, i.e., the poor initialization and the presence of outliers, are eliminated. Furthermore, this modified clustering technique enables us to determine the number of subsystems without any prior knowledge about system. In addition, applying the structure of the state-input domain, that is, considering the time sequence of input-output pairs, provides a more efficient clustering algorithm, which is the other novelty of this work. Finally, the proposed algorithm has been evaluated by parameter identification of an IGV servo actuator. Simulation together with experiment analysis has proved the effectiveness of the proposed method.
Highlights
1 Introduction Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors; in other words, at different time intervals, different dynamical behaviors can be expected from a hybrid system
5 Conclusions In this paper, an effective method for identification of piecewise affine system is proposed. This method uses the clustering of feature vectors that consist of parameter vectors corresponding to local datasets and average spatial position of each one
In practice, the data acquired from a system being identified are received sequentially within a specific time interval, each piece of data can be assigned a label, time tag, which shows the sequence of data relative to one another in the time domain
Summary
Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors; in other words, at different time intervals, different dynamical behaviors can be expected from a hybrid system. By presenting an approach based on regressor vector clustering in [13], authors have assigned the data to the appropriate region, and they have determined the subsystem corresponding to each region. First by using the structure of the stateinput domain, that is, considering the time sequence of input-output pairs, some appropriate LDs are created This is important, because in practice always the sequence of generation of data points is known. This is the motivation to introduce the concept of “time tag”, the label assigned to each data point to identify the sequence of them Using these labels, one can create some appropriate LDs. Second, the application of two novel methods, i.e., fuzzy PCA-guided robust k-means clustering algorithm [23], along with a neighborhood outlier detection algorithm [24] is studied. By applying this assumption, which, in practice, is always satisfied automatically, the data can be divided into smaller groups with similar properties
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