Continuous-Time and Event-Triggered Online Optimization for Linear Multi-Agent Systems

TL;DR

This paper introduces a decentralized online optimization approach for linear multi-agent systems that achieves low regret and fit bounds, incorporating event-triggered communication to reduce overhead without Zeno behavior.

Contribution

It presents a novel distributed saddle-point controller for multi-agent systems with time-varying costs and constraints, incorporating event-triggered communication to improve efficiency.

Findings

Achieves constant regret bound in decentralized optimization.

Ensures sublinear fit bound with event-triggered communication.

Maintains performance with no Zeno behavior in discrete updates.

Abstract

This paper studies the decentralized online convex optimization problem for heterogeneous linear multi-agent systems. Agents have access to their time-varying local cost functions related to their own outputs, and there are also time-varying coupling inequality constraints among them. The goal of each agent is to minimize the global cost function by selecting appropriate local actions only through communication between neighbors. We design a distributed controller based on the saddle-point method which achieves constant regret bound and sublinear fit bound. In addition, to reduce the communication overhead, we propose an event-triggered communication scheme and show that the constant regret bound and sublinear fit bound are still achieved in the case of discrete communications with no Zeno behavior. A numerical example is provided to verify the proposed algorithms.with no Zeno behavior. A numerical example is provided to verify the proposed algorithms.