# Scale-free weak output synchronization of multi-agent systems with adaptive protocols

arXiv: https://arxiv.org/abs/2512.06278 · HTML: https://mlsanity.com/paper/2512.06278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Learning When to Act: Interval-Aware Reinforcement Learning with Predictive Temporal Structure](https://mlsanity.com/paper/2603.22384/) (2026)

## Abstract (arXiv)

In this paper, we study output synchronization for multi-agent systems. The objective is to design a protocol which only depends on the agent dynamics and does not require any knowledge of the network. If the network has a directed spanning tree then the protocols designed in this paper achieve classical output synchronization. Otherwise, the protocol achieves weak synchronization which is induced by network stability in the sense that the signals exchanged over the network converge to zero. Weak sychronization is explained in detail in this paper. Even though we consider linear agents, it is known that this in general requires nonlinear protocols. In the paper we use adaptive protocols. In the literature, two classes of protocols are considered often called collaborative protocols (with additional communication between the protocols and non-collaborative protocols (sometimes referred to as fully decentralized where the additional communication is not present). This paper considers both of these cases.