Distributed online optimization for heterogeneous linear multi-agent systems with coupled constraints

TL;DR

This paper develops a distributed online optimization method for heterogeneous multi-agent systems with coupled constraints, achieving low regret and fit bounds, noise tolerance, and reduced communication via event-triggered mechanisms.

Contribution

It introduces a continuous-time distributed controller with saddle-point techniques for heterogeneous agents, extending to event-triggered communication and analyzing noise robustness.

Findings

Achieves constant regret and sublinear fit bounds similar to centralized methods.

Maintains performance under measurement noise if noise is not excessive.

Reduces communication frequency without sacrificing theoretical guarantees.

Abstract

This paper studies a class of distributed online convex optimization problems for heterogeneous linear multi-agent systems. Agents in a network, knowing only their own outputs, need to minimize the time-varying costs through neighboring interaction subject to time-varying coupled inequality constraints. Based on the saddle-point technique, we design a continuous-time distributed controller which is shown to achieve constant regret bound and sublinear fit bound, matching those of the standard centralized online method. We further extend the control law to the event-triggered communication mechanism and show that the constant regret bound and sublinear fit bound are still achieved while reducing the communication frequency. Additionally, we study the situation of communication noise, i.e., the agent's measurement of the relative states of its neighbors is disturbed by a noise. It is shown that, if the noise is not excessive, the regret and fit bounds are unaffected, which indicates the controller's noise-tolerance capability to some extent. Finally, a numerical simulation is provided to support the theoretical conclusions.