Abstract
In this article, the enumeration method and the expectation maximization (EM) algorithm are combined for the identification of linear parameter varying (LPV) systems with unknown time-varying system delays. The unknown system delays are addressed as the latent variables which are assumed to be uniformly distributed in the possible value range. At each sampling instant, by using the basic idea of the enumeration method, the unknown delay is estimated by maximizing its posterior distribution function (PDF). Moreover, the problem of outliers is also considered in the identification procedure and the robust t-distribution instead of the common Gaussian distribution is used to handle the data abnormality. All the equations to estimate the unknown parameters and the delays are all derived by using the EM algorithm. The validity and robustness of the proposed approach are demonstrated by using several simulation examples.
Highlights
System identification (SI) belongs to the discipline which grabs the process model from the process data by using the pre-chosen principles [1]–[3]
The considered linear parameter varying (LPV) model was represented as the linear SS form, and the model parameters were all represented as the combination of power functions of the scheduling variable
This paper considers the robust identification of LPV models with time-varying system delays
Summary
System identification (SI) belongs to the discipline which grabs the process model from the process data by using the pre-chosen principles [1]–[3]. This paper considers the robust identification of LPV models with time-varying system delays. The identification of ARX model with constant system delay is introduced in [3] and the unknown delay and the model parameters are estimated simultaneously in the identification process. 1) The generalized identification method for LPV model with time-varying delays is proposed and it is suitable for the constant system delay case; 2) To ensure the robustness of the proposed method, the Student’s t-distribution is adopted to model the complicated measurement noise by adaptively adjusting its DOF parameter; 3) The formulas to simultaneously estimate the timevarying system delays and the model parameters are derived in the identification steps. The rest sections of this paper are arranged as: Section II describes the main identification problem of this work in detail; Section III gives the detailed steps of the desired algorithm; Section IV reveals the robustness and validity of the desired algorithm through several tests; Section V presents the final conclusions of current paper
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