A study of algorithms for identifying parameters of a dynamical system approximating time series

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A study of algorithms for identifying parameters of a dynamical system approximating time series

 

Author: Leung, Shing-keung
Title: A study of algorithms for identifying parameters of a dynamical system approximating time series
Degree: M.Sc.
Year: 1999
Subject: Differentiable dynamical systems
Algorithms
Time-series analysis
Hong Kong Polytechnic University -- Dissertations
Department: Multi-disciplinary Studies
Dept. of Applied Mathematics
Pages: vii, 74 leaves : ill. ; 30 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1484339
URI: http://theses.lib.polyu.edu.hk/handle/200/1656
Abstract: The objectives of this project are to study algorithms for identifying parameters of a dynamical system, and to apply these algorithms to approximate a given time series. The artificial neural network approach, the optimal control approach, and the system identification approach are reviewed. Algorithms are derived and implemented with Matlab for simulating and predicting time series, in particular, the sunspots and the Mackey-Glass series. The data series are transformed to the same degree before being tested by the derived algorithms so that comparisons can be made regarding the merits of different algorithms. Computer experiments give good results using the artificial neural network algorithms. With the same degree of data transformation of the test sequences for comparison purpose, the results are not as good but seem acceptable using the optimal control algorithms, and the system identification algorithms. Regarding numerical stability of algorithms, the artificial neural network approach guarantees stability and convergence. In the optimal control approach, stability has not been rigorously proved. Depending on the choice of the weighting matrix for optimal control, the plots of sum of squared errors with iterations could show oscillatory components decreasing with iterations. In the system identification approach, experiment results indicate that stability could be a concerned issue.

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