Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Cluster Flows and Multiagent Technology

Version 1 : Received: 27 November 2020 / Approved: 30 November 2020 / Online: 30 November 2020 (08:09:24 CET)

A peer-reviewed article of this Preprint also exists.

Granichin, O.; Uzhva, D.; Volkovich, Z. Cluster Flows and Multiagent Technology. Mathematics 2021, 9, 22. Granichin, O.; Uzhva, D.; Volkovich, Z. Cluster Flows and Multiagent Technology. Mathematics 2021, 9, 22.

Journal reference: Mathematics 2020, 9, 22
DOI: 10.3390/math9010022

## Abstract

Multiagent technologies give a new way to study and control complex systems. Local interactions between agents often lead to group synchronization also known as clusterization, which usually is a more rapid process in comparison with relatively slow changes in external environment. Usually, the goal of system control is defined by the behaviour of a system on long time intervals. When these time intervals are much longer than the time of cluster formation, clusters may be considered as new variables in a slow'' time model. We call such variables mesoscopic'' to emphasize their scale laying between the level of the whole system (macroscopic scale) and the level of individual agents (microscopic scale). Thus, it allows us to reduce significantly the dimensionality of a system by omitting considerations of each separated agent, so that we may hope to reduce the required amount of control inputs. Thus, we are often able to consider a system as a collection of flowing'' (morphing) clusters emerged form behaviour of a huge amount of individual agents. In this paper, we contrast such approach to the one where a system is considered as a network of elementary agents. We develop a mathematical framework for analysis of cluster flows in multiagent networks and use it to analyze the Kuramoto model as an attracting example of a complex networked system. In this model, a clusterization leads to sparse representation of dynamic trajectories in the whole quantized state space. With that in mind, compressive sensing allows to restore the trajectories in a high-dimensional discrete state space based on significantly lower amount of randomized integral mesoscopic observations. We propose a corresponding algorithm of quantized dynamic trajectory compression. It could allow us to efficiently transmit the state space data to a data center for further control synthesis. The theoretical results are illustrated for a simulated multiagent network with multiple clusters.

## Subject Areas

cluster flows; mesoscopic observations; data compression

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