Evolution of clusters in large-scale dynamical networks

Proskurnikov, Anton V.; Granichin, Oleg

doi:10.35470/2226-4116-2018-7-3-102-129

Cited by 15 publications

(17 citation statements)

References 228 publications

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“…As an alternative to the accepted statistical methodology, the current article suggests an agent-based approach designed to overcome this practice's limitations. In the agent-oriented framework, a complex system (called a multiagent system) is considered as a network of simple autonomous units (called intelligent agents or simple agents), and the system of interacting agents [24] [25] [26]. The current study aims to develop a unified general theory connecting the macroscopic scale of the whole system and the individual components' microscopic scale.…”

Section: Multiagent Systemsmentioning

confidence: 99%

Cluster Flows and Multiagent Technology

Granichin¹,

Uzhva²,

Volkovich³

2020

Preprint

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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.

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Section: Multiagent Systemsmentioning

confidence: 99%

Cluster Flows and Multiagent Technology

Granichin¹,

Uzhva²,

Volkovich³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…As an alternative to the accepted statistical methodology, the current article suggests an agent-based approach designed to overcome this practice's limitations. In the agent-oriented framework, a complex system (called a multiagent system) is respected as an arrangement of basic independent elements (termed intelligent agents or just agents), which communicate to each other [23][24][25]. The current study intends to suggest a unified general theory connecting the macroscopic scale of the whole system and the individual components' microscopic scale.…”

Section: Multiagent Systemsmentioning

confidence: 99%

“…Because dynamic systems usually describe multiagent networks, the synchronization state signifies a convergence of dynamic trajectories to some unique synchronized one. This consequence is well studied in the case of linear systems [23,30,31]. The more general case of nonlinear control rules is first considered in [32], where the Kuramoto model of coupled oscillators is analyzed as an example of a system with nonlinear dynamics.…”

Section: Multiagent Systemsmentioning

confidence: 99%

“…where N is the number of agents and M is the number of clusters, which is supposed to be of the same order as the sparsity of the system. In this paper, we reformalize the framework of multiagent networks proposed in [23] and refined in [32], aiming to apply compressive sensing for efficient observations of dynamic trajectories. For this purpose, in the current work, we propose an algorithm, on the first step of which the trajectories are quantized, then compressed.…”

Section: Multiagent Systemsmentioning

confidence: 99%

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Cluster Flows and Multiagent Technology

2020

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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.

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“…The basic approach to the analysis of dynamics of complex and network systems is the decomposition method [Bullo, Cortes and Martinez, 2009;Frolov, Koronovskii, Makarov, Maksimenko, Goremyko and Hramov, 2017;Lakshmikantham, Leela and Martynyuk, 1989;Matrosov, 2001;Proskurnikov and Granichin, 2018;Siljak, 1991;Zubov, 1970]. The method is effectively used in various forms for the investigation of mechanical systems, see, for instance, [Andrievsky and Boikov, 2017;Alyshev, Dudarenko and Melnikov, 2018;Matrosov, 2001;Merkin, 1974] and the bibliography therein.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of gyroscopic systems with discrete and distributed delays

Aleksandrov

Semenov

Zhan

2019

CAP

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This paper provides stability analysis results for a linear mechanical system with a large parameter at the vector of gyroscopic forces and with delay in positional forces. Both cases of discrete and distributed delay are studied. Using the decomposition method and Lyapunov-Krasovskii functionals, conditions are found under which delay does not disturb the asymptotic stability of the considered system. The effectiveness of the obtained results is illustrated by a simulation example.

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Evolution of clusters in large-scale dynamical networks

Cited by 15 publications

References 228 publications

Cluster Flows and Multiagent Technology

Cluster Flows and Multiagent Technology

Cluster Flows and Multiagent Technology

Stability analysis of gyroscopic systems with discrete and distributed delays

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