A clustering-based approach for the identification of a class of temporally switched linear systems

The behaviours of hybrid dynamic systems (HDS) are determined by combining continuous variables with discrete switching logic. The identification of a HDS aims to find an accurate model of the system’s dynamics based on its past inputs and outputs. In pattern recognition (PR) methods, each mode is represented by a set of similar patterns that form restricted regions in the feature space. These sets of patterns are called classes. A pattern is a vector built from past inputs and outputs. HDS identification is a challenging problem since it involves the estimation of different sets of parameters without knowing in advance which sections of the measured data correspond to the different modes of the system. Therefore, HDS identification can be achieved by combining two steps: clustering and parameter estimation. In the clustering step, the number of discrete modes (i.e., the classes that input–output data points belong) is estimated. The parameter estimation step finds the parameters of the models that govern the continuous dynamics in each mode. In this paper, an unsupervised PR method is proposed to achieve the clustering step of the identification of temporally switched linear HDS. The determination of the number of modes does not require prior information about the modes or their number.

► We considered the identification of temporally switched linear ARX model. ► The proposed approach does not require the knowledge about the number of modes. ► The proposed approach can be used to achieve off-line and on-line identification. ► The proposed approach overcomes the problem of initialization.