Abstract
To project digital companies of the Industry 4.0 is a production task which requires to implement in the industrial infrastructure the elements of multi-agent environment. Multi-agent environment is components (cyber and physical systems) of two elements: the automatic one in physical level and program one (model) in the virtual level. Physical element is a digital system of automatic control. The program one is a code fragment to describe the functionality of cyber and physical system with a mathematical model. There is a scheme of physical and virtual cyber and physical system components interaction for digital automatic production of the Industry 4.0. The properties of the Industry 4.0 production company (a smart factory) depends on the interaction scheme of the digital company infrastructure. Cyber and physical systems interaction scheme is generated in a smart factory cloud. There are some options of cyber and physical systems topology which are good for the Industry 4.0 production infrastructure.
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