Robust Sparse Identification of Linear Parameter‐Varying Systems Using Variational Bayesian With Spike‐and‐Slab Prior

ABSTRACT This article considers the robust sparse identification problem of linear parameter‐varying (LPV) systems within the framework of the variational Bayesian (VB) algorithm. Considering that the order of the LPV model and the dependencies between the parameters and the scheduling variable are unknown, an over‐parameterization approach is adopted to construct the model representation. As a result, this leads to model redundancy and sparsity. To address this issue, the spike‐and‐slab (SS) prior is introduced to characterize the model parameters, enabling the acquisition of a sparse solution and thereby determining the true orders and structure of the LPV model. Subsequently, an auxiliary model is utilized to estimate the noise‐free output within the information vector. Additionally, a Student's t distribution is employed to handle outliers in the measured output, leading to a robust sparse identification algorithm. Finally, the proposed identification algorithm is effectively validated through a simulation example and the cascaded tank system.