Self-Tuning Approach to Stabilizing Unknown and Unstable Periodic Orbits

Takumi HASEGAWA  Tadashi TSUBONE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.11   pp.2212-2217
Publication Date: 2014/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.2212
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
controlling chaos,  unknown and unstable periodic orbits,  stability transformation method,  1-dimensional return map,  

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Summary: 
We consider an improved control method based on the Stability Transformation Method. Stability Transformation Method detects unknown and unstable periodic orbits of chaotic dynamical systems. Based on the approach to realize the Stability Transformation Method in real systems, we have proposed a control method which can stabilize unknown and unstable periodic orbits embedded in chaotic attractors. However, setting of the control parameters of the control system has remained as unsolved issue. When the dynamics of a target system are unknown, the control parameters have to be set by trial and error. In this paper, we improve the control method with the automatic adjustment function of the control parameters. We show an example of stabilizing unstable periodic orbits of the 3-dimensional hysteresis chaos generator by using the proposed control method. Some results are confirmed by laboratory measurements. The results imply that any unknown and unstable periodic orbits can be stabilized by using the proposed method, if the target chaos system is reduced to 1-dimensional return map.