Optimal approximation of linear systems using Taguchi-sliding-based differential evolution algorithm

A Taguchi-sliding-based differential evolution algorithm (TSBDEA) is proposed in this study to solve the problem of optimally approximating linear systems. The TSBDEA is an approach of combining the differential evolution algorithm (DEA) with the Taguchi-sliding-level-method (TSLM). In the TSBDEA, the TSLM is to provide a new systematic crossover operation for breeding better offspring, and consequently enhances the DEA. By using the proposed TSBDEA, 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 an error criterion is minimized. Numerical examples show that the presented TSBDEA gives an effective and robust way for obtaining optimal reduced-order models for stable/unstable and/or nonminimum-phase complex systems, and can get better results than the existing DEA-based method reported in the literature.