Research of Stability and Convergence of Decentralized Coordination of Local Control of Distributed Cyber-physical Systems

Abstract

The use of decentralized coordination of state control of distributed cyber-physical systems with continuous objects, in which, in addition to the physical interaction of the elements of a continuous object, there is information interaction of local coordinators as part of agents of a multi-agent system, leads to the formation of multi-loop control systems. The features of decentralized coordination control of such systems (nonlinearity of coordinators, mutual physical impact of the elements of the object, the presence of production costs of the accumulated resource, which determines the state of the elements, etc.) necessitate additional studies of the stability of the system and the convergence of the coordination process. The aim of the work is to study the conditions of stability and convergence of decentralized coordination of a distributed cyber-physical control system with a wave coordination method. A condition for the stability of such systems is obtained. The model of a system of two connected controllable elements and local control systems has been developed. The transfer function of the system is obtained using the method of equivalent transformations. It is shown that in the absence of coordination, such system is stable under the condition of attenuation under the propagation of influences on the elements of a continuous object. The stability and convergence of decentralized coordination of local control systems with the wave coordination method based on a simulation model is investigated using the example of three-element systems. The simulation model was created in the Scilab/Xcos system. As a result of the studies, it was shown that although the system is stable, the state of the object's elements coincides with the specified one, however, the duration of the coordination process significantly exceeds the duration of the transient processes of individual elements. Further research is supposed to be directed at the proof the hipotesis that the stability of the system independent of the number of controlled elements of a continuous object and studying the conditions for the stability of active systems (with an increase in the influence in the process of propagation).