Applying differential transformation method to parameter identification problems

Authors:
Ming-Jyi Jang;Jiun-Shen Wang;Yung-Chin Liu
Affiliations:
Department of Automation and Control, Far East College, Tainan 704, Taiwan, ROC;Department of Mechanical Engineering, Far East College, Tainan, Taiwan, ROC;Department of Mechanical Engineering, Industrial Technology Research Institute, Taiwan, ROC
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

A direct search algorithm to find the maximum likelihood estimate for parameter identification problems is proposed in this paper. The parameter identification criterion function is constructed by differential transform, and an algorithm for adjustment of the unknown parameters is selected and used to identify the parameters in such a way that the criterion function is minimized. This method has the following advantages: (1) The spectra of system model can be obtained with the unknown parameter and the initial value of state variable, therefore, the criterion function can be constructed from the above spectra. (2) The problem of singularity and sensitivity in solving traditional inverse problems can be avoided. (3) The solving process is performed in iteration and is easily realized in the numerical computation. (4) Both linear and nonlinear problems can be solved with the same process.