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Optimal approximation of linear systems by a differential evolution algorithm

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2 Author(s)
Shih-Lian Cheng ; Dept. of Chem. Eng., Nat. Cheng Kung Univ., Tainan, Taiwan ; Hwang, Chyi

The problem of optimally approximating linear systems is solved by a differential evolution algorithm (DEA) incorporating a search-space expansion scheme. The optimal approximate rational model with/without a time delay for a system described by its rational or irrational transfer function is sought such that a frequency-domain L2-error criterion is minimized. The distinct feature of the proposed model approximation approach is that the search-space expansion scheme can enhance the possibility of converging to a global optimum in the DE search. This feature and the chosen frequency-domain error criterion make the proposed approach quite efficacious for optimally approximating unstable and/or nonmimimum-phase linear systems. The simplicity and robustness of the modified DEA in terms of easy implementation and minimum assumptions on search space are demonstrated by two numerical examples

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Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on  (Volume:31 ,  Issue: 6 )