Small-Gain Theorem Based Distributed Prescribed-Time Convex Optimization For Networked Euler-Lagrange Systems

TL;DR

This paper introduces a novel distributed prescribed-time convex optimization method for networked Euler-Lagrange systems, utilizing small-gain theory and adaptive controllers to achieve convergence within a preset time.

Contribution

It develops a new prescribed-time stabilization approach based on small-gain criteria, enabling distributed convex optimization with guaranteed convergence time for Euler-Lagrange systems.

Findings

Proposed a prescribed-time small-gain criterion for system stabilization.

Designed adaptive prescribed-time local tracking controllers.

Validated the approach with a numerical example.

Abstract

In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local objective function and local information interactions among neighboring agents, a set of auxiliary systems is constructed to cooperatively seek the optimal solution. The DPTCO problem is then converted to the prescribed-time stabilization problem of an interconnected error system. A prescribed-time small-gain criterion is proposed to characterize prescribed-time stabilization of the system, offering a novel approach that enhances the effectiveness beyond existing asymptotic or finite-time stabilization of an interconnected system. Under the criterion and auxiliary systems, innovative adaptive prescribed-time local tracking controllers are designed for subsystems. The prescribed-time convergence lies in the introduction of time-varying gains which increase to infinity as time tends to the prescribed time. Lyapunov function together with prescribed-time mapping are used to prove the prescribed-time stability of closed-loop system as well as the boundedness of internal signals. Finally, theoretical results are verified by one numerical example.