Robust LPV System Identification With Skewed and Asymmetric Measurement Noise

Abstract

In this study, the skewed and asymmetric measurement noise is considered and solved in the identification of linear parameter varying (LPV) systems and a new robust global identification framework is established based on the shifted asymmetric Laplace (SAL) measurement distribution. The skewness and tails of the SAL distribution can be adaptively adjusted by the hyperparameters, that means the statistical property of the SAL distribution is governed by the hyperparameters which makes the SAL distribution flexible to resist various types of outliers including the skewed and asymmetric noise. The mathematical formulations of the identification problem are realized by the expectation maximization (EM) algorithm and the maximum likelihood estimates of the parameters are produced. It is realized that both the model parameters and the hyperparameters are extracted directly from the collected identification data. Compared with the existing robust methods, the advantages and disadvantages of the current work are revealed through the designed verification tests performed on the numerical example and the three-tank system, and the main results of this paper are also summarized.Note to Practitioners—The LPV system is widely applied in industrial processes due to its flexible capability of describing the complex nonlinear dynamics. For the probability-based identification of LPV systems, the Gaussian, Laplace and Student’s t distributions are commonly used to describe the output noise. But all of them exhibit symmetric statistical properties which may limit their applications in practical industrial settings, will them keep effective for the skewed and asymmetric measurement noise? Motivated by this question, this paper solves the robust identification of LPV systems with skewed and asymmetric measurement noise and a new robust global identification approach is introduced based on the SAL distribution. In this paper, it is proved that the common Laplace distribution can be seen as a special case of the SAL distribution. That means the proposed method is robust not only for the skewed and asymmetric measurement noise but also for the outliers, which could extend its applications in practical industrial processes. The tests performed on the numerical example and the three-tank system verify the proposed approach.