Generalized continuous mixed p‐norm based sliding window algorithm for a bilinear system with impulsive noise

• Published in: International journal of robust and nonlinear control Vol. 32; no. 13; pp. 7663 - 7681
• Main Authors: Liu, Wentao, Xiong, Weili
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.09.2022
• Subjects: Algorithms; Bilinear system; Canonical forms; Cost function; generalized continuous mixed p$$ p $$‐norm; impulsive noise; Norms; Parameter estimation; Sliding; sliding window; State observers
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6236

This article investigates the identification issue of the bilinear system in the presence of the impulsive noise. The bilinear system based on the observer canonical form is translated into a regressive form, and a bilinear state observer is established to estimate the state variables. To overcome the effects of the impulsive noise to parameter estimation, the proposed algorithms employ a generalized continuous mixed p$$ p $$‐norm cost function, which can generate an adjustable gain that control the proportions of the error norms without resorting to a priori knowledge of the noise. Moreover, a sliding window is designed to update the dynamical data by removing the oldest data and adding the newest measurement data. An numerical example exhibits that the proposed algorithms can reduce the impact of the impulsive noise to parameter estimation and improve the parameter estimation accuracy compared with the conventional algorithms.