Oscillations in Mixed-Feedback Systems

TL;DR

This paper introduces a novel method for analyzing limit cycle oscillations in mixed-feedback systems by reformulating the problem as a zero-finding task involving mixed-monotone relations, demonstrated on the Van der Pol oscillator.

Contribution

It presents a new approach that leverages convex optimization techniques to efficiently analyze oscillations in mixed-feedback systems.

Findings

Method effectively computes limit cycles in mixed-feedback systems.

Demonstrated on the Van der Pol oscillator with promising results.

Utilizes existing algorithms for difference of convex functions.

Abstract

A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two maximally monotone relations. The problem can then be solved efficiently by borrowing existing algorithms that minimize the difference of two convex functions. The potential of the method is illustrated on the classical Van der Pol oscillator.