EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

CHARACTERISATION OF CHAOS IN CHUA'S OSCILLATOR IN TERMS OF UNSTABLE PERIODIC ORBITS

1993 ◽  
Vol 03 (02) ◽  
pp. 411-429 ◽  
Author(s):  
MACIEJ J. OGORZAŁEK ◽  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Picture Book ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Canonical Chua’S Circuit

We present a picture book of unstable periodic orbits embedded in typical chaotic attractors found in the canonical Chua's circuit. These include spiral Chua's, double-scroll Chua's and double hook attractors. The "skeleton" of unstable periodic orbits is specific for the considered attractor and provides an invariant characterisation of its geometry.

TIME DELAYED REPETITIVE LEARNING CONTROL FOR CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (05) ◽  
pp. 1057-1065 ◽  
Author(s):  
YANXING SONG ◽  
XINGHUO YU ◽  
GUANRONG CHEN ◽  
JIAN-XIN XU ◽  
YU-PING TIAN
Keyword(s):  
Periodic Orbits ◽  
Adaptive Learning ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Learning Control ◽  
Control Technique ◽  
Unstable Periodic Orbits ◽  
Repetitive Learning ◽  
Control Principle

In this paper, a time-delayed chaos control method based on repetitive learning is proposed. A general repetitive learning control structure based on the invariant manifold of the chaotic system is given. The integration of the repetitive learning control principle and the time-delayed chaos control technique enables adaptive learning of appropriate control actions from learning cycles. In contrast to the conventional repetitive learning control, no exact knowledge (analytic representation) of the target unstable periodic orbits is needed, except for the time delay constant, which can be identified via either experiments or adaptive learning. The controller effectively stabilizes the states of the continuous-time chaos on desired unstable periodic orbits. Simulations on the Duffing and Lorenz chaotic systems are provided to verify the design and analysis.

Controlling the Chaotic n-Scroll Chua's Circuit

2003 ◽  
Vol 13 (09) ◽  
pp. 2709-2714 ◽  
Author(s):  
Yan-Li Zou ◽  
Xiao-Shu Luo ◽  
Pin-Qun Jiang ◽  
Bing-Hong Wang ◽  
Guanrong Chen ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Fixed Points ◽  
Chaos Control ◽  
Control Method ◽  
Chua’S Circuit ◽  
System Matrix ◽  
Chua's Circuit ◽  
State Variable ◽  
Different Types ◽  
Linearized System

In this paper, controlling chaos in the chaotic n-scroll Chua's circuit is studied. The approach taken is to use feedback of a single state variable in a simple PD (proportional and differential) format. First, the unstable fixed points in the n-scroll Chua's circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points. Then, the controllability of these two-types of fixed points is studied. Theoretical analysis shows that the first type of unstable fixed points can be stabilized, at which Hopf bifurcation can also be generated. Control results of the n-scroll Chua's circuit are then demonstrated. Both theoretical analysis and numerical simulation results show that the proposed chaos control method is indeed effective.

scholarly journals Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor

2007 ◽  
Vol 12 (4) ◽  
pp. 469-477 ◽  
Author(s):  
A. Boukabou ◽  
A. Chebbah ◽  
A. Belmahboul
Keyword(s):  
System Dynamics ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

This paper addresses the control of the n-scroll Chua’s circuit. It will be shown how chaotic systems with multiple unstable periodic orbits (UPOs) detected in the Poincar´e section can be stabilized as well as taking the system dynamics from one UPO to another.

EXPERIMENTAL MODIFICATIONS OF VOA-BASED AUTONOMOUS AND NONAUTONOMOUS CHUA'S CIRCUITS FOR HIGHER DIMENSIONAL OPERATION

2006 ◽  
Vol 16 (09) ◽  
pp. 2649-2658
Author(s):  
RECAI KILIÇ
Keyword(s):  
Experimental Method ◽  
Operational Amplifier ◽  
Experimental Results ◽  
High Dimensional ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Voltage Mode ◽  
Pspice Simulation ◽  
Chua Circuit ◽  
Higher Dimensional

In order to operate in higher dimensional form of autonomous and nonautonomous Chua's circuits keeping their original chaotic behaviors, we have experimentally modified VOA (Voltage Mode Operational Amplifier)-based autonomous Chua's circuit and nonautonomous MLC [Murali–Lakshmanan–Chua] circuit by using a simple experimental method. After introducing this experimental method, we will present PSpice simulation and experimental results of modified high dimensional autonomous and nonautonomous Chua's circuits.

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

EXPERIMENTAL STUDY OF CFOA-BASED INDUCTORLESS CHUA'S CIRCUIT

2004 ◽  
Vol 14 (04) ◽  
pp. 1369-1374 ◽  
Author(s):  
RECAI KILIÇ
Keyword(s):  
Experimental Study ◽  
High Frequency ◽  
Chaotic Behavior ◽  
Comparative Investigation ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Current Feedback ◽  
Chua's Circuit ◽  
Op Amps ◽  
High Frequency Performance

The current feedback op amps (CFOAs), with some significant advantages over the conventional op amps, have been used instead of voltage op amps (VOAs) in new implementations of Chua's circuit. In our previous study, after providing a comparative investigation of CFOA-based realizations of Chua's circuit in the literature, we have also presented an alternative inductorless CFOA-based realization of Chua's circuit, and the circuit's chaotic behavior by Pspice simulations. In this paper, we investigate CFOA-based Chua's circuit by constructing an experimental setup, and testing the performance of the proposed implementation at different frequencies. Its excellent high frequency performance was experimentally verified.

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