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MATOUŠEK, R. HŮLKA, T.
Original Title
Stabilization of Higher Periodic Orbits of the Chaotic Logistic and Henon Maps using Meta-evolutionary Approaches
Type
conference paper
Language
English
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.
Keywords
Orbits; Mathematical model; Logistics; Linear programming; Chaos; Sociology; Statistics
Authors
MATOUŠEK, R.; HŮLKA, T.
Released
8. 8. 2019
Publisher
IEEE
Location
NEW YORK
ISBN
978-1-7281-2153-6
Book
2019 IEEE Congress on Evolutionary Computation, CEC 2019 - Proceedings
Pages from
1758
Pages to
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", pages="1758--1765", publisher="IEEE", address="NEW YORK", doi="10.1109/CEC.2019.8790075", isbn="978-1-7281-2153-6" }