An iterative tangential interpolation algorithm for model reduction of MIMO systems

TL;DR

This paper introduces an iterative tangential interpolation algorithm for reducing large-scale MIMO systems, leveraging adaptive weight optimization and low-rank interpolation to improve approximation accuracy and computational efficiency.

Contribution

The paper presents a novel iterative algorithm that combines tangential interpolation with adaptive weight optimization and low-rank techniques for MIMO system reduction.

Findings

Monotonically decreasing weighted H2 error norm during interpolation

Multiple algorithms with trade-offs between complexity and performance

Performance comparable to standard model reduction methods

Abstract

We consider model reduction of large-scale multi-input, multi-output (MIMO) systems using tangential interpolation in the frequency domain. Our scheme is related to the recently-developed Adaptive Antoulas--Anderson (AAA) algorithm, which is an iterative algorithm that uses concepts from the Loewner framework. Our algorithm has two main features. The first is the use of freedom in interpolation weight matrices to optimize a proxy for an \(H_2\) system error. The second is the use of low-rank interpolation, where we iteratively add low-order interpolation data based on several criteria including minimizing maximum errors. We show there is freedom in the interpolation point selection method, leading to multiple algorithms that have trade-offs between computational complexity and approximation performance. We prove that a weighted \(H_2\) norm of a representative error system is monotonically decreasing as interpolation points are added. Finally, we provide computational results and some comparisons with prior work, demonstrating performance on par with standard model reduction methods.