Regularization, Recognition and Complexity Estimation Methods of Automata Models of Discrete Dynamical Systems in Control Problem

摘要

In paper are considered laws of functioning of discrete determined dynamical systems and specific processes of functioning of such systems. As basic mathematical model of laws of functioning of systems are used automata models with a fundamentally new extension of these models to models with a countable infinite sets of states. This expansion is possible thanks to the proposed and developed by Tverdohlebov V. A. the mathematical apparatus of geometrical images of automaton mappings. Are presented results of development of regularization methods for partially set automata models of systems based on use of geometrical images of automatons mappings and numerical interpolation methods. Also in paper are considered a problem of complexity estimation of laws in a whole and specific processes of functioning of dynamic systems. For these purpose are used recurrent models and methods and also a specific mathematical apparatus of discrete riv-functions. Is spent classification by complexity estimations of automata models.