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Variational Bayesian identification for bilinear state space models with Markov‐switching time delays
Author(s) -
Fei Qiuling,
Ma Junxia,
Xiong Weili,
Guo Fan
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5190
Subject(s) - bilinear interpolation , markov chain , state space , control theory (sociology) , markov model , mathematics , observer (physics) , state space representation , state (computer science) , discrete time and continuous time , sequence (biology) , continuous time markov chain , markov process , computer science , bayesian probability , mathematical optimization , algorithm , variable order markov model , control (management) , artificial intelligence , statistics , physics , quantum mechanics , biology , genetics
Summary This article studies the parameter identification problem for bilinear state space models with time‐varying time delays. Considering the correlation of time delays, the Markov chain switching mechanism is adopted to model the delay sequence. Based on the observer canonical form, the bilinear state space model is transformed into a regressive form. A bilinear state observer is designed to estimate the state variables. Under the variational Bayesian scheme, the system parameters, discrete delays, and the Markov transition probabilities are identified by using the measurement data. A numerical example and a continuous stirred tank reactor simulation are employed to validate the effectiveness of the proposed algorithm.