15. Identification of a Class of Hybrid Dynamic Systems

The behavior of hybrid dynamic systems (HDS) switches between several modes with different dynamics involving both discrete and continuous variables in the course of time. Their identification aims at finding an accurate model of the system dynamics based on its past inputs and outputs. The identification can be achieved by two steps: the clustering and the regression. The clustering step aims at the estimation of the mode (discrete state) of each input–output data point as well as the switching sequence among these modes. The regression step determines the sub-models controlling the dynamic (continuous states) in each mode. In Pattern Recognition (PR) methods, each mode is represented by a set of similar patterns forming restricted regions in the feature space, called classes. A pattern is a vector built from past inputs and outputs. In this chapter, we propose to use an unsupervised PR method to realize the clustering step of the identification of switched linear HDS. The determination of the number of modes as well as the switching sequence does not require any information in advance about the modes, for example, their distribution, their shape, …, or their number.