Distributed Adaptive Time-Varying Optimization with Global Asymptotic Convergence

TL;DR

This paper introduces a distributed adaptive algorithm for multi-agent systems that ensures global asymptotic convergence to optimal solutions in time-varying environments, relaxing previous assumptions and reducing waiting times.

Contribution

The paper presents a novel distributed algorithm combining an average estimator and adaptive optimizer with a Dead Zone Algorithm, enabling convergence without Hessian knowledge and faster implementation.

Findings

Proves global asymptotic convergence under mild conditions.

Relaxed the need for Hessian information of cost functions.

Demonstrated effectiveness through two example applications.

Abstract

In this note, we study distributed time-varying optimization for a multi-agent system. We first focus on a class of time-varying quadratic cost functions, and develop a new distributed algorithm that integrates an average estimator and an adaptive optimizer, with both bridged by a Dead Zone Algorithm. Based on a composite Lyapunov function and finite escape-time analysis, we prove the closed-loop global asymptotic convergence to the optimal solution under mild assumptions. Particularly, the introduction of the estimator relaxes the requirement for the Hessians of cost functions, and the integrated design eliminates the waiting time required in the relevant literature for estimating global parameter during algorithm implementation. We then extend this result to a more general class of time-varying cost functions. Two examples are used to verify the proposed designs.