Evolution of clusters in large-scale dynamical networks

Abstract

Recent tremendous progress in electronics, complexity theory and network science provides new opportunities for intellectual control of complex large-scale systems operating in turbulent environment via networks of interconnected miniature devices, serving as actuators, sensors and data processors. Actual dynamics of the resulting control systems are too sophisticated to be examined controlled by traditional methods, which primarily deal with ordinary differential equations. However, their complexity can be dramatically reduced by fast processes, organizing the elementary units of the system (called agents) into relatively small number of clusters. The clusters emerge and deteriorate in response to changes in the environment, and the processes of their formation and destruction are very short in time. During the periods of the clusters’ existence, the system’s dynamics is essentially low-dimensional due to synchronization between the agents in each cluster. An enormously complicated system is thus reduced to a finite-dimensional model with time-varying structure of the state vector. The low-dimensionality of the reduced model allows to control it by using classical methods, e.g. model-predictive or adaptive control. This philosophy of complex systems control is illustrated on an experimental setup, called the “airplane with feathers”. The wings of this airplane are equipped with arrays of microsensors, microcomputers, and microactuators (“feathers”). The feathers self-organize into clusters by using a multi-agent consensus protocol; the aim of this coordination is to reduce the perturbing forces, affecting the airplane in a turbulent flow.