Open AccessRecurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems
Author(s) -
Alexander Slabospitsky
Publication year - 2018
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2018/3.10
Subject(s) - mathematics , least squares function approximation , moment (physics) , inverse , matrix (chemical analysis) , bilinear interpolation , norm (philosophy) , representation (politics) , variable (mathematics) , operator (biology) , mathematical analysis , statistics , biochemistry , physics , geometry , materials science , chemistry , classical mechanics , repressor , estimator , politics , political science , transcription factor , law , composite material , gene
The estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.