ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Application of Statistic Methods for Estimation of Control Times for Determinate Dynamical Systems


Sergey Mikhailovich Khryashchev

Saint-Petersburg State Polytechnic University,
Doctor of Physics and Mathematics, professor,
29 Politechnicheskaya,
195251, Saint-Petersburg, Russia


Dynamical control systems generated by hyperbolic maps are considered. Basic concept of measure theory, control theory, and theory of stochastic processes are used for description of these systems. Existence of trajectories dense in the state space and local controllability along these trajectories ensure full controllability for the systems. In the paper, we propose a method for estimation of control times of dynamical systems. This method is based on analysis of sequences of accessibility sets and their volumes. By use of statistic methods, it is possible obtain estimates of control times. These estimates are more exactly than previously obtained estimates for similar systems.

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