# Cluster Flows and Multiagent Technology

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Saint Petersburg State University and Institute for Problems in Mechanical Engineering Russian Academy of Sciences, St. Petersburg 190000, Russia

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Software Engineering Department, ORT (Obchestvo Remeslenogo Truda) Braude Academic College of Engineering, Karmiel 2161002, Israel

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Author to whom correspondence should be addressed.

Received: 27 November 2020 / Revised: 12 December 2020 / Accepted: 18 December 2020 / Published: 24 December 2020

(This article belongs to the Special Issue Machine Learning and Data Mining in Pattern Recognition)

Multiagent technologies provide a new way for studying and controlling complex systems. Local interactions between agents often lead to group synchronization, also known as clusterization (or clustering), which is usually a more rapid process in comparison with relatively slow changes in external environment. Usually, the goal of system control is defined by the behavior of a system on long time intervals. As is well known, a clustering procedure is generally much faster than the process of changing in the surrounding (system) environment. In this case, as a rule, the control objectives are determined by the behavior of the system at large time intervals. If the considered time interval is much larger than the time during which the clusters are formed, then the formed clusters can be considered to be “new variables” in the “slow” time model. Such variables are called “mesoscopic” because their scale is between the level of the entire system (macro-level) and the level of individual agents (micro-level). Detailed models of complex systems that consist of a large number of elementary components (miniature agents) are very difficult to control due to technological barriers and the colossal complexity of tasks due to their enormous dimension. At the level of elementary components of systems, in many applications it is impossible to verify the models of the agent dynamics with the traditionally high degree of accuracy, due to their miniaturization and high frequency of control actions. The use of new mesoscopic variables can make it possible to synthesize fewer different control inputs than when considering the system as a collection of a large number of agents, since such inputs will be common for entire clusters. In order to implement this idea, the “clusters flow” framework was formalized and used to analyze the Kuramoto model as an attracting example of a complex nonlinear networked system with the effects of opportunities for the emergence of clusters. It is shown that clustering leads to a sparse representation of the dynamic trajectories of the system, which makes it possible to apply the method of compressive sensing in order to obtain the dynamic characteristics of the formed clusters. The essence of the method is as follows. With the dimension N of the total state space of the entire system and the a priori assignment of the upper bound for the number of clusters s, only m integral randomized observations of the general state vector of the entire large system are formed, where m is proportional to the number s that is multiplied by logarithm $N/s$ . A two-stage observation algorithm is proposed: first, the state space is limited and discretized, and compression then occurs directly, according to which reconstruction is then performed, which makes it possible to obtain the integral characteristics of the clusters. Based on these obtained characteristics, further, it is possible to synthesize mesocontrols for each cluster while using general model predictive control methods in a space of dimension no more than s for a given control goal, while taking the constraints obtained on the controls into account. In the current work, we focus on a centralized strategy of observations, leaving possible decentralized approaches for the future research. The performance of the new framework is illustrated with examples of simulation modeling.

*Keywords:*cluster flows; mesoscopic observations; data compression