Model reduction by balanced truncation of dominant Lure systems

TL;DR

This paper introduces a novel model reduction method for systems exhibiting switching and oscillatory behaviors, leveraging dominance theory and balanced truncation to effectively approximate non-equilibrium dynamics.

Contribution

It develops a dominance-preserving model reduction technique for Lure systems, extending classical balanced truncation to systems with non-linear feedback.

Findings

Successfully approximates oscillatory heat flow control system

Extends balanced truncation to non-linear feedback systems

Provides a framework for analyzing non-equilibrium behaviors

Abstract

The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for non-equilibrium behaviors. The proposed framework addresses this need by exploiting recent advances on dominance theory. Classical balanced truncation for linear time-invariant systems is used to develop a dominance-preserving model reduction method for Lure systems, i.e. systems that can be decomposed as the feedback interconnection of a linear system and a static nonlinearity. The method is illustrated by approximating the oscillatory behavior of a discretized heat flow control system.