Gradient-Based Stochastic Extremum-Seeking Control for Multivariable Systems with Distinct Input Delays

TL;DR

This paper introduces a novel gradient-based stochastic extremum-seeking control method for multivariable systems with arbitrary, distinct input delays, ensuring stability and convergence without backstepping transformations.

Contribution

It presents a delay-compensated extremum-seeking approach with phase and predictor feedback, simplifying design and achieving delay- and system-dimension-independent convergence.

Findings

Achieves local exponential stability with arbitrary input delays.

Provides delay- and system-dimension-independent convergence rates.

Demonstrates robust performance through numerical example.

Abstract

This paper addresses the design and analysis of a multivariable gradient-based stochastic extremum-seeking control method for multi-input systems with arbitrary input delays. The approach accommodates systems with distinct time delays across input channels and achieves local exponential stability of the closed-loop system, guaranteeing convergence to a small neighborhood around the extremum point. By incorporating phase compensation for dither signals and a novel predictor-feedback mechanism with averaging-based estimates of the unknown gradient and Hessian, the proposed method overcomes traditional challenges associated with arbitrary, distinct input delays. Unlike previous work on deterministic multiparameter extremum-seeking with distinct input delays, this stability analysis is achieved without using backstepping transformations, simplifying the predictor design and enabling a more straightforward implementation. Specifically, the direct application of Artstein's reduction approach results in delay- and system-dimension-independent convergence rates, enhancing practical applicability. A numerical example illustrates the robust performance and advantages of the proposed delay-compensated stochastic extremum-seeking method.