Gradient Free Cooperative Seeking of a Moving Source

TL;DR

This paper introduces a gradient-free cooperative control method for a network of agents to track a moving source in a time-varying scalar field, combining extremum seeking and formation control for faster convergence.

Contribution

It presents a novel composite control law that integrates extremum seeking with formation control, and provides a convergence analysis under specific field conditions.

Findings

Proves convergence to a bounded neighborhood of the moving extrema.

Demonstrates improved convergence speed through formation control.

Supports theoretical results with numerical simulations.

Abstract

In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field's time varying extrema. We assume the time-varying field satisfies the Polyak Lojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results.