Multivariable Stochastic Newton-Based Extremum Seeking with Delays

TL;DR

This paper introduces a Newton-based stochastic extremum-seeking control method that effectively handles multi-input systems with delays, ensuring stability and convergence through predictor feedback and Hessian estimation.

Contribution

It develops a novel delay-compensating extremum-seeking approach combining predictor-based feedback with stochastic Hessian inverse estimation for multi-input systems.

Findings

Ensures exponential stability and convergence near the extremum.

Effectively handles long input delays in multi-input systems.

Demonstrates robustness through numerical simulations.

Abstract

This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic perturbations to enable delay compensation with user-defined convergence rates. The method ensures exponential stability and convergence near the unknown extremum, even under long delays. It extends to multi-input, single-output systems with cross-coupled channels. Stability is analyzed using backstepping and infinite-dimensional averaging. Numerical simulations demonstrate its effectiveness in handling time-delayed channels, showcasing both the challenges and benefits of real-time optimization in distributed parameter settings.