Learning in Dynamic Environments: Application to the Identification of Hybrid Dynamic Systems

The behavior of Hybrid Dynamic Systems (HDS) switches between several modes with different dynamics over time. Their identification aims at finding the model mapping the inputs to real-valued outputs. Generally, the identification is divided into tow steps: clustering and regression. In the clustering step, the discrete modes, i.e. classes, that each input-output data point belongs to as well as the switching sequence among these modes are estimated. The regression step aims at finding the models governing the continuous dynamic in each mode. In this paper, we propose an approach to achieve the clustering step of the identification of the switched HDS. In this approach, the number of discrete modes, classes, and the switching sequence among them are estimated using an unsupervised Pattern Recognition (PR) method. This estimation is achieved without the need to any prior information about these modes, e.g. their shape or distribution, or their number.