Composite Dynamical System for Controlling Chaos

Tetsushi UETA; Hiroshi KAWAKAMI

Composite Dynamical System for Controlling Chaos

Tetsushi UETA, Hiroshi KAWAKAMI

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We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C⁰. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E78-A No.6 pp.708-714

Publication Date: 1995/06/25

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Type of Manuscript: PAPER

Category: Systems and Control

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Tetsushi UETA, Hiroshi KAWAKAMI, "Composite Dynamical System for Controlling Chaos" in IEICE TRANSACTIONS on Fundamentals, vol. E78-A, no. 6, pp. 708-714, June 1995, doi: .
Abstract: We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C⁰. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e78-a_6_708/_p

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@ARTICLE{e78-a_6_708,
author={Tetsushi UETA, Hiroshi KAWAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Composite Dynamical System for Controlling Chaos},
year={1995},
volume={E78-A},
number={6},
pages={708-714},
abstract={We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C⁰. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Composite Dynamical System for Controlling Chaos
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 708
EP - 714
AU - Tetsushi UETA
AU - Hiroshi KAWAKAMI
PY - 1995
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E78-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1995
AB - We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C⁰. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.
ER -