Optimal Stationary Synchronization of Heterogeneous Linear Multi-Agent Systems

TL;DR

This paper introduces optimal stationary synchronization (OSS) for heterogeneous linear multi-agent systems, allowing for non-zero steady-state errors and energy-efficient synchronization within bounds, relaxing traditional exact synchronization requirements.

Contribution

It proposes a novel OSS method combining bounded exosystem synchronization with local LQT, enabling energy-efficient, bounded-error synchronization in heterogeneous networks.

Findings

Allows agents to participate despite non-zero steady-state errors

Balances synchronization error with input-energy consumption

Guarantees error bounds with time-invariant optimal control

Abstract

In this paper, we address the output synchronization of heterogeneous linear networks. In the literature, all agents are typically required to synchronize exactly to a common trajectory. Here, we introduce optimal stationary synchronization (OSS) instead which permits non-zero steady-state synchronization errors. As a benefit, we are able to relax standard requirements. E.g., agents are allowed to participate in the network even when they usually cannot synchronize exactly. In addition, OSS enables agents to save input-energy by synchronizing within tolerable error-bounds. Our new method combines the synchronization of bounded exosystems with local infinite-time linear quadratic tracking (LQT). This results in an optimal balance of each agent's synchronization error versus its consumed input-energy. Moreover, we extend recent results in LQT such that the derived time-invariant optimal control guarantees that the synchronization error satisfies given strict bounds. All these aspects are demonstrated by an illustrative simulation example with a detailed analysis.