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

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

Estimates of Transport Times for Nonstationary Systems Generated by Quasilinear Hyperbolic Maps

Author(s):

Sergey Mikhailovich Khryashchev

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

khrya@hotbox.ru

Abstract:

Chaotic control systems and regular control systems differ essential. For chaotic system, there exist everywhere dense trajectories and it makes possible to use arbitrarily small control actions to reach a goal of control. In the paper, some characteristics of state of chaos are considered and classification of chaotic system is given.
Weakly chaotic systems are studied separately. These systems appear by degeneration of strongly chaotic systems. In the paper, asymptotic estimations are given for transport times using arbitrarily small control actions.
The estimations are obtained by analysis of sequences of volumes of sets of accessibility and they are expressed in the term of characteristics of control system.

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