Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from attraction points for non-linear dynamic systems under non-classical assumptions
DOI:
https://doi.org/10.17721/1812-5409.2024/2.10Keywords:
discrete-time non-linear dynamic system, recurrent time-varying parameter estimation, non-classical assumptions, attraction points, Moore – Penrose pseudo-inversion operator, least squares method with variable forgetting factor, weighted residual sum of squaresAbstract
For discrete non-linear dynamic systems, the problem of optimal estimation of non-stationary parameters that can slowly change over time is considered. The method of least squares with a variable forgetting factor is used to estimate the unknown parameters of the above-mentioned objects. The situation is considered when the classical assumptions that guarantee the uniqueness of this estimate may be violated. In previous publications, the estimate that has the smallest euclidean norm, i.e. the smallest deviation from the zero vector, was analyzed as a unique estimate on the set of all such estimates. Explicit and recurrent forms of representation were obtained for it. A recurrent procedure for calculating the value of the corresponding residual sum of squares was also proposed. In this paper, on the set of all optimal estimates, the estimate that has the least deviation from the given attraction points at each moment of time was taken as a unique estimate. An explicit form of representation through the Moore-Penrose pseudo-inversion operator is given for this estimate. A convenient recurrent form of representation for it is also obtained, which allows to speed up the calculation process, because it no longer requires the use of either the Moore-Penrose matrix pseudo-inversion operation, or even the usual matrix inversion operation. The presented recurrent algorithm for the corresponding weighted residual sum of squares will be useful for quality control of the obtained mathematical model. The proposed recurrent procedures for recalculating the optimal estimate of non-stationary parameters with the least deviation from the given attraction points and the weighted residual sum of squares will allow to significantly speed up the process of estimating non-stationary parameters in the on-line mode for discrete nonlinear dynamic systems in case of possible violation of classical assumptions and avoid the need to calculate Moore-Penrose pseudo-inverse matrices.
Pages of the article in the issue: 59 - 64
Language of the article: Ukrainian
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