Abstract
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.
Highlights
IntroductionIt is common in a sociological (or physical) investigation to differ amid three primary societal (or system) levels: the micro-level, the meso-level, and the macro-level
It is common in a sociological investigation to differ amid three primary societal levels: the micro-level, the meso-level, and the macro-level
Compression algorithms are incredebly relevant nowadays, since they allow for speeding up information exchange at fixed bandwith: e.g., MP3 [8,9] allows for getting rid of unnecessary high sound frequencies in music, while JPEG [10,11] reduces the picture file size at the cost of coarsening high frequency components that are responsible for small details
Summary
It is common in a sociological (or physical) investigation to differ amid three primary societal (or system) levels: the micro-level, the meso-level, and the macro-level. A meso-level study is provided for groups lying in their size amid the micro and macro levels, and often explicitly invented in order to disclose relations between micro and macro levels Following this general taxonomy, we can analogously consider the Information (Digital) Age (a famous appellation of the modern period) as the macro-level Industrial Revolution, expressed by a quick transmission from the traditional industry to the massive application of information technology. It takes place due to the known crisis of the modern scientific look at the “picture of the world” Aiming to handle this global difficulty, it seems reasonable to primarily pay attention to an appropriate theory that is based on a suitable mathematical model. Psychology and cybernetics make attempts to do so; the further it goes, the harder it is to track the relation between a complex cognitive system and its fundamental components
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