A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics
Masayasu Suzuki; Noboru Sakamoto
Kybernetika (2015)
- Volume: 51, Issue: 1, page 4-19
- ISSN: 0023-5954
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topSuzuki, Masayasu, and Sakamoto, Noboru. "A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics." Kybernetika 51.1 (2015): 4-19. <http://eudml.org/doc/270034>.
@article{Suzuki2015,
abstract = {In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.},
author = {Suzuki, Masayasu, Sakamoto, Noboru},
journal = {Kybernetika},
keywords = {symbolic dynamics; chaos control; global stability; symbolic dynamics; chaos control; global stability},
language = {eng},
number = {1},
pages = {4-19},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics},
url = {http://eudml.org/doc/270034},
volume = {51},
year = {2015},
}
TY - JOUR
AU - Suzuki, Masayasu
AU - Sakamoto, Noboru
TI - A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 1
SP - 4
EP - 19
AB - In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.
LA - eng
KW - symbolic dynamics; chaos control; global stability; symbolic dynamics; chaos control; global stability
UR - http://eudml.org/doc/270034
ER -
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