Abstract Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.
Received: 15 October 2006
Revised: 31 January 2007
Accepted manuscript online:
PACS:
05.45.Gg
(Control of chaos, applications of chaos)
Fund: Project supported by the
National Natural Science Foundation of China (Grant No
60374013), the Doctorate Foundation of Henan Polytechnic
University, China (Grant No 648606).
Cite this article:
Song Yun-Zhong (宋运忠) The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors 2007 Chinese Physics 16 1918
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