Adaptive Extremum Seeking Using Recursive Least Squares

TL;DR

This paper introduces a recursive least squares-based extremum seeking scheme that improves convergence speed and robustness over traditional gradient-based methods, applicable to static and dynamic systems with scalar or vector parameters.

Contribution

It develops and analyzes a novel RLS-based extremum seeking approach, demonstrating asymptotic convergence and enhanced performance over existing methods.

Findings

Proven asymptotic convergence for all cases.

Simulation results validate improved convergence speed.

Enhanced robustness to measurement noise.

Abstract

Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are typically observed to be superior, in terms of convergence speed and robustness to measurement noises, over gradient algorithms, it is expected that LS based ES schemes will also provide faster convergence and robustness to sensor noises. In this paper, with this motivation, a recursive least squares (RLS) estimation based ES scheme is designed and analysed for application to scalar parameter and vector parameter static map and dynamic systems. Asymptotic convergence to the extremum is established for all the cases. Simulation studies are provided to validate the performance of proposed scheme.