Control of Multichaotic Systems Using the Extended OGY Method
Abstract
This paper considers the problem of controlling coupled chaotic maps. Coupled chaotic maps or multichaotic subsystems are complex dynamical systems that consist of several chaotic sub-systems with interactions. The OGY methodology is extended to deal with the control of such systems. It is shown that the decentralized control design scheme in which the individual controllers share no information is not generally able to control multichaotic systems. Simulation results are used to support the main conclusions of the paper.
References
- Chaos 8 , 596 ( 2002 ) . Crossref, Web of Science, Google Scholar
- Physica D 139 , 87 ( 2000 ) . Crossref, Google Scholar
- IEEE Trans. Circuits Syst.-I 44 , 971 ( 1997 ) . Crossref, Web of Science, Google Scholar
- Commun. Math. Phys. 50 , 69 ( 1976 ) . Crossref, Web of Science, Google Scholar
- Physica D 150 , 163 ( 2001 ) . Crossref, Web of Science, Google Scholar
-
L. Jentoft and Y. Li , Stabilizing the Henon Map with the OGY Algorithm ( Olin College of Engineering , 2008 ) . Google Scholar -
K. Kaneko and I. Tsuda , Complex Systems — Chaos and Beyond: A Constructive Approach with Applications in Life Science ( Springer , 2001 ) . Crossref, Google Scholar -
J. M. Maciejowski , Multivariable Feedback Design ( Addison Wesley , 1989 ) . Google Scholar -
H. Matano , S. Ushiki and M. Yamagut , Discrete Population Models and Chaos ,Lecture Notes in Numerical and Applied Analysis 2 ( 1980 ) . Google Scholar - Phys. Rev. Lett. 64 , 1196 ( 1990 ) . Crossref, Web of Science, Google Scholar
- Chaos Solit. Fract. 40 , 1376 ( 2009 ) . Crossref, Web of Science, Google Scholar
- Paula, A. S. [2010] "Control of chaos in mechanical systems," PhD thesis, Federal Rio de Janeiro University . Google Scholar
- Int. J. Non-Lin. Mech. 46 , 1076 ( 2011 ) . Crossref, Web of Science, Google Scholar
-
S. Skogestad and I. Postlethwaite , Multivariable Feedback Control: Analysis and Design ( Wiley , 2005 ) . Google Scholar - Witvoet, G. [2005] "Control of chaotic dynamical systems using OGY," Traineeship Report, Eindhoven University of Technology . Google Scholar
-
H. Zhang , D. Liu and Z. Wang , Controlling Chaos — Suppression, Synchronization and Chaotification ( Springer , 2009 ) . Google Scholar