Publication detail
Stabilization of Higher Periodic Orbits of the Chaotic Logistic and Henon Maps using Meta-evolutionary Approaches
MATOUŠEK, R. HŮLKA, T.
English title
Stabilization of Higher Periodic Orbits of the Chaotic Logistic and Henon Maps using Meta-evolutionary Approaches
Type
conference paper
Language
en
Original abstract
This paper deals with an advanced adjustment of stabilization sequences for selected discrete chaotic systems by means of meta-evolutionary approaches. As the representative models of deterministic chaotic systems, one dimensional Logistic equation and two dimensional H ' enon map were used. The stability of the chaotic systems has been studied by computer simulations. The novelty of the approach is in an effective design of a new type of objective function, which is very important for the whole optimization process of higher periodic orbits. Furthermore, modern meta-heuristics were used for own design of proper stabilizing sequences. The used optimization methods are a grid-based Nelder-Mead Algorithm (NMA), Genetic Algorithm (GA) as well as Genetic Programming (GP). GP results show good capability of control law synthesis in case of higher periodic orbits. A connection of GP and second level optimization using GA or NMA displays better results than stand alone meta-heuristic techniques. Although the task of stabilizing the presented chaotic systems is known, its solution presented for periodic orbits two and four is not trivial.
English abstract
This paper deals with an advanced adjustment of stabilization sequences for selected discrete chaotic systems by means of meta-evolutionary approaches. As the representative models of deterministic chaotic systems, one dimensional Logistic equation and two dimensional H ' enon map were used. The stability of the chaotic systems has been studied by computer simulations. The novelty of the approach is in an effective design of a new type of objective function, which is very important for the whole optimization process of higher periodic orbits. Furthermore, modern meta-heuristics were used for own design of proper stabilizing sequences. The used optimization methods are a grid-based Nelder-Mead Algorithm (NMA), Genetic Algorithm (GA) as well as Genetic Programming (GP). GP results show good capability of control law synthesis in case of higher periodic orbits. A connection of GP and second level optimization using GA or NMA displays better results than stand alone meta-heuristic techniques. Although the task of stabilizing the presented chaotic systems is known, its solution presented for periodic orbits two and four is not trivial.
Keywords in English
Orbits; Mathematical model; Logistics; Linear programming; Chaos; Sociology; Statistics
Released
08.08.2019
Publisher
IEEE
Location
NEW YORK
ISBN
978-1-7281-2153-6
Book
2019 IEEE Congress on Evolutionary Computation, CEC 2019 - Proceedings
Pages from–to
1758–1765
Pages count
8
BIBTEX
@inproceedings{BUT162169,
author="Radomil {Matoušek} and Tomáš {Hůlka},
title="Stabilization of Higher Periodic Orbits of the Chaotic Logistic and Henon Maps using Meta-evolutionary Approaches",
booktitle="2019 IEEE Congress on Evolutionary Computation, CEC 2019 - Proceedings
",
year="2019",
month="August",
pages="1758--1765",
publisher="IEEE",
address="NEW YORK",
isbn="978-1-7281-2153-6"
}