Identification of hybrid system based on Probability weighted multiple ARX model

This paper proposes a probability weighted ARX (PrARX) model wherein the multiple ARX models are composed by the probabilistic weighting functions. As the probabilistic weighting function, a `softmax´ function is introduced. Then, the parameter estimation problem for the proposed model is formulated as a single optimization problem. Furthermore, the identified PrARX model can be easily transformed to the corresponding PWARX model with complete partitions between regions. Finally, the proposed model is applied to the modeling of the driving behavior, and the usefulness of the model is verified.