Hierarchical identification of nonlinear hybrid systems in a Bayesian framework

Abstract

This paper presents a hierarchical framework for the identification of nonlinear hybrid systems in the form of Switched Nonlinear AutoRegressive models with eXogenous variables (SNARX). The identification is done via three levels of inference, using Bayes' rule. In the first level, model parameters are computed via a Maximum a Posteriori (MAP) estimator. The posterior distribution therein involved depends on hyper-parameters that are tuned in the second level of inference. Such terms determine model complexity, and the Bayesian framework is key in returning values that trade off complexity with accuracy by automatically embodying the Occam's razor principle. Lastly, the third level compares different model structures by means of a quality measure that encompasses data fitness, model complexity, and data classification. The proposed framework is compared with existing relevant methods and is tested on different numerical models, showing promising performance.