Iterative Identification for Multivariable Systems with Time-Delays Based on Basis Pursuit De-Noising and Auxiliary Model

• Main Authors: Junyao You, Yanjun Liu
• Format: Article
• Language: English
• Published: MDPI AG 2018-11-01
• Series: Algorithms
• Subjects: multivariable system; parameter identification; time-delay estimation; basis pursuit de-noising; auxiliary model; quadratic program
• Online Access: https://www.mdpi.com/1999-4893/11/11/180

This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm.