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Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator
Author(s) -
Liu Siyu,
Zhang Yanliang,
Ding Feng,
Alsaedi Ahmed,
Hayat Tasawar
Publication year - 2020
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3166
Subject(s) - observability , bilinear interpolation , algorithm , least squares function approximation , mathematics , state vector , iterative method , system identification , state space , estimator , identification (biology) , estimation theory , mathematical optimization , computer science , data modeling , statistics , physics , botany , classical mechanics , database , biology
Summary Because of the product item of the control input and the state vector, the identification of bilinear systems is difficult. This paper considers the combined parameter and state estimation problems of bilinear state‐space systems. On the basis of the observability canonical form and the model transformation, an identification model with a linear combination of the system parameters is obtained. Using the hierarchical principle, the identification model is decomposed into three submodels with fewer variables, and a three‐stage least squares‐based iterative (3S‐LSI) algorithm is presented to estimate the system parameters. Furthermore, we derive a state estimator (SE) for estimating the unknown states, and present an SE‐3S‐LSI algorithm for estimating the unknown parameters and states simultaneously. After that, the least squares‐based iterative algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can identify the bilinear system effectively but the 3S‐LSI algorithm can improve the computational efficiency. The simulation results indicate the effectiveness of the proposed algorithms.