scholarly journals Chaos control based on stability Transformation method for unstable periodic orbits

2012 ◽  
Vol 3 (2) ◽  
pp. 246-256 ◽  
Author(s):  
Yuki Kawai ◽  
Tadashi Tsubone
Keyword(s):  
Periodic Orbits ◽  
Chaos Control ◽  
Transformation Method ◽  
Unstable Periodic Orbits ◽  
Stability Transformation Method

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.

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.

scholarly journals PULSATING FEEDBACK CONTROL FOR STABILIZING UNSTABLE PERIODIC ORBITS IN A NONLINEAR OSCILLATOR WITH A NONSYMMETRIC POTENTIAL

2007 ◽  
Vol 17 (08) ◽  
pp. 2797-2803 ◽  
Author(s):  
G. LITAK ◽  
M. ALI ◽  
L. M. SAHA
Keyword(s):  
Feedback Control ◽  
Periodic Orbits ◽  
Efficient Method ◽  
Chaotic Attractor ◽  
Nonlinear Oscillator ◽  
Chaos Control ◽  
Degree Of Freedom ◽  
Unstable Periodic Orbits ◽  
Periodic State

We examine a strange chaotic attractor and its unstable periodic orbits in case of one-degree of freedom nonlinear oscillator with nonsymmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsating feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.

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