Cooperative information space distributed macromodels

Abstract

The paper introduces a new approach for the dynamic distributed modelling using the variation principle, applied to a functional on trajectories of random process, and its connection to the process's information functional. The model equations in partial derivatives (PDE) are found by the solution of the variation problem for this functional. This allows us to build a two-level information model with a random process at the microlevel and dynamic process at the macrolevel. The informational macromodels are connected to the equations of irreversible thermodynamics and kinetics. The paper focuses on the problem of a space-time consolidation, which is a new area in the PDE theory, directly connected to modelling complex systems. The synthesized cooperative distributed macromodel is formed during the optimal time-spaced movement, directed toward the equalization and collectivization of the model operator eigenvectors. The mathematical formalism has been applied for the constructive solution to the problems of the object identification, combined with optimal control's synthesis and process’ consolidation. The procedure, demonstrated on this paper's examples and cooperative macromodels, leads to the creation of a dynamic information hierarchical network. The developed computer-based methodology and software were practically used for systems modelling, identification, and control of a diversity of information interactions in some physical (technological) and non-physical (economical and information) objects.