Publication detail
Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution
MATOUŠEK, R. MINÁŘ, P.
Czech title
Stabilizace chaotické logistické rovnice pomocí algoritmů HC12 a gramatické evoluce
English title
Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution
Type
journal article - other
Language
en
Original abstract
The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors. The chaotic system stabilization is based on time-delay auto-synchronization (TDAS, ETDAS) and proper combination with own synthesized control law. This synthesized chaotic controller is based on one or two compensator. The primary compensator generates the perturbation sequence using TDAS/ETDAS method, second one is own design using method of GE. The original design of the objective function takes inspiration from standard control theory. All tests are performed using Matlab/Simulink environment.
Czech abstract
Článek pojednává o nových možnostech stabilizace chaotockých systémů. Stabilizace je prezentována na modelu logistické rovnice. Je využito jak zavedeného disturbančního principu ETDAS, tak vlastní hybridní koncepce ve formě kompenzující sekvence navržené pomocí GE a HC12.
English abstract
The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors. The chaotic system stabilization is based on time-delay auto-synchronization (TDAS, ETDAS) and proper combination with own synthesized control law. This synthesized chaotic controller is based on one or two compensator. The primary compensator generates the perturbation sequence using TDAS/ETDAS method, second one is own design using method of GE. The original design of the objective function takes inspiration from standard control theory. All tests are performed using Matlab/Simulink environment.
Keywords in Czech
zpožďované zpětnovazebné řízení, ETDAS, TDAS, logistická rovnice, gramatická evoluce, HC12, optimalizace
Keywords in English
Delayed feedback control; Deterministic chaos; ETDAS; Grammatical evolution; HC12; Logistic equation; Metaheuristic optimization; TDAS
RIV year
2013
Released
01.06.2013
Publisher
Springer
Location
Germany
ISSN
2194-5357
Volume
2013
Number
210
Pages from–to
137–146
Pages count
10
BIBTEX
@article{BUT107090,
author="Radomil {Matoušek} and Petr {Minář},
title="Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution",
year="2013",
volume="2013",
number="210",
month="June",
pages="137--146",
publisher="Springer",
address="Germany",
issn="2194-5357"
}