Optimal approximation of linear systems by a differential evolution algorithm

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