Multimodel Bayesian estimation for LPV time-delay systems with incomplete observations

A multimodel Bayesian approach to identifying linear parameter-varying (LPV) systems subject to piecewise input time-delays, outliers and randomly missing observations is developed in this article. The global nonlinearity is characterized by weighted combination of multiple submodels, where each local-model identity is treated as hidden variable to represent the working mode of the system. To tackle data anomaly problems, the Student’s t-distribution is utilized to model the observations containing outliers, and the missing part of the output is regarded as another hidden variable. By introducing weighting coefficient to indicate the significance of each delay, the piecewise input time-delay can be automatically chosen irrespective of its initial interval. All required quantities, including the identities of local-model and time-delay, the missing values of the outputs, and the local-model parameters with their uncertainties, are comprehensively updated using variational Bayesian (VB) approach. Subsequently, a numerical study and the irrigation channel are adopted to prove the validity of the presented method.