Extremum Seeking for Stabilization of Systems Not Affine in Control

TL;DR

This paper extends extremum seeking control techniques to stabilize nonlinear systems where control enters through a nonlinear function, broadening applicability beyond affine-in-control systems.

Contribution

It develops stabilizing controllers for non-affine control systems using extremum seeking, addressing a gap in existing methods that only handle affine systems.

Findings

Successfully stabilizes non-affine systems using ESC

Extends ESC applicability to practical nonlinear systems

Provides theoretical foundation for non-affine control stabilization

Abstract

In [22] a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC the extremum seeker itself controls the systems through feedback rather than fine tuning a controller. The ESC results, and other related results, apply only to systems affine in control. However, in most physical systems the control effort enters the system's dynamics through a nonlinear function, such as an input with deadline and saturation. In this work, we utilize our previous results on ESC to develop stabilizing controllers for systems of practical interest that are non-affine in control.