2023/09/30 by Jared Jonas, Jonas, Jared, Bassam Bamieh +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #Model Reduction and Neural Networks #Numerical methods for differential equations #Real-time simulation and control systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2310.00309
openalex publication_date 2023/09/30 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28
We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which can be viewed as a type of moment-matching technique for system realization and approximation. We consider variations on this algorithm that are suitable for model reduction of linear time invariant systems while addressing some of the shortcomings of the block-AAA variant of the algorithm for MIMO systems. In particular, we develop state-space formulas and keep track of the state-space dimension at every step of the adaptive block-AAA algorithm, showing an unfavorable increase of the state dimension. We propose a new low-rank adaptive interpolation algorithm that addresses this shortcoming. Comparative computational results are included for the algorithms above, together with comparisons to balanced reduction.