Review and analysis of model order reduction techniques for high-dimensional complex systems

Complex practical system designs pose significant challenges from a research perspective, often resulting in high computational requirements for analysis. Model order reduction (MOR) is a valuable technique to address this issue. This study provides a comprehensive review of the literature on MOR, focusing specifically on high-dimensional complex systems. It examines the fundamental theories and limitations of established MOR methods, including the Factor division method, Pade approximation (PA) method, Stability equation (SE) method, Differentiation method, and Routh approximation (RA) method. The study also investigates the frequency domain approach for obtaining a reduced-order model (ROM). Among the MOR methods, the PA method is a widely studied and practical approach that aims to retain the crucial dynamics of a high-dimensional complex system. This survey presents a detailed discussion of the PA method for obtaining the ROM. Additionally, six test systems are analyzed to compare the step and frequency responses generated by various MOR strategies. The integral square error criterion is used to assess the effectiveness of the reduction procedures. Finally, the study proposes a new system abatement method based on Atomic Orbital Search (AOS) optimization for obtaining the ROM of large-scale linear time-invariant (LTI) systems and designing controllers based on the reduced order model.