Optimal Modal Truncation

TL;DR

This paper presents an optimization-based approach to modal truncation, focusing on dominant poles relative to system norms, and reformulates the problem as a convex integer program, supported by numerical examples.

Contribution

It introduces a novel optimization framework for modal truncation based on dominant poles and reformulates it as a convex integer program.

Findings

Effective identification of dominant poles for system reduction

Convex integer programming formulation of modal truncation

Numerical examples demonstrating the approach's practicality

Abstract

This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation problem. The latter is reformulated as an equivalent convex integer or mixed-integer program. Numerical examples highlight the concept and optimisation approach.