Model recovery for multi-input signal-output nonlinear systems based on the compressed sensing recovery theory

• Published in: Journal of the Franklin Institute Vol. 359; no. 5; pp. 2317 - 2339
• Main Authors: Ji, Yan, Kang, Zhen, Zhang, Xiao, Xu, Ling
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.03.2022; Elsevier Science Ltd
• Subjects: Algorithms; Autoregressive models; Data recovery; Estimation; Filtration; Impulse response; Input output analysis; Matched pursuit; MISO (control systems); Nonlinear systems; Parameter identification; Regression analysis; White noise
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2022.01.032

This paper considers the parameter and order estimation for multiple-input single-output nonlinear systems. Since the orders of the system are unknown, a high-dimensional identification model and a sparse parameter vector are established to include all the valid inputs and basic parameters. Applying the data filtering technique, the input-output data are filtered and the original identification model with autoregressive noise is changed into the identification model with white noise. Based on the compressed sensing recovery theory, a data filtering-based orthogonal matching pursuit algorithm is presented for estimating the system parameters and the orders. The presented method can obtain highly accurate estimates from a small number of measurements by finding the highest absolute inner product. The simulation results confirm that the proposed algorithm is effective for recovering the model of the multiple-input single-output Hammerstein finite impulse response systems.