Singularly Perturbed Averaging with Application to Bio-Inspired 3D Source Seeking

TL;DR

This paper analyzes a class of oscillatory systems relevant to extremum seeking, providing explicit averaging formulas, convergence proofs, and introducing a bio-inspired 3D source seeking algorithm with stability guarantees.

Contribution

It offers explicit averaging formulas and convergence analysis for singularly perturbed oscillatory systems, and introduces a novel bio-inspired 3D source seeking method with stability proof.

Findings

Explicit averaging formulas derived for the class of systems.

Proven convergence of system trajectories to averaged reduced systems.

Proposed 3D source seeking algorithm demonstrated with stability.

Abstract

We analyze a class of singularly perturbed high-amplitude, high-frequency oscillatory systems that arises in extremum seeking applications. We provide explicit formulas for averaging and establish the convergence of the trajectories of this class of systems to the trajectories of a suitably averaged reduced order system by combining the higher order averaging theorem with singular perturbation techniques. Finally, we propose a novel bio-inspired 3D source seeking algorithm and establish its singular practical stability.