通过线性增量控制抑制混沌

Suppressing chaos by linear augmentation control

中文关键词  线性增量控制  吸引子退化  混沌抑制

英文关键词  linear augmentation control  degenerating attractors  chaos suppression

中文摘要

      本文基于三维Lorenz两翼系统、三维四翼系统以及四维四翼系统, 利用线性增量控制实现了减少吸引子涡 卷数以及抑制混沌的目的. 此控制是在多涡卷混沌系统中耦合一个线性系统, 通过不断增强两个系统之间的耦合 强度, 移动并且逐渐消除多涡卷混沌系统的部分平衡点, 从而达到控制目标. 利用平衡点坐标变化曲线、分岔图、Ly -apunov指数谱、以及相轨图等表征方法分析并刻画了被控制的多涡卷系统动力学行为变化的过程. 为了验证线性 增量控制对于实现吸引子退化以及抑制混沌的有效性和电路可实现性, 以三维四翼系统的控制为例设计了电路, Multism仿真结果和硬件实验结果均与在MATLAB中得到的数值仿真结果一致.

英文摘要

      In this paper, the control purpose of degenerating multi-scroll attractors and suppressing chaos is realized through linear augmentation control based on three chaotic systems, including a 3D Lorenz two-wing system, a 3D fourwing system and a 4D four-wing system. By increasing the coupling strength between the two systems, partial equilibrium points of the multi-scroll chaotic system are moved and gradually eliminated. The system dynamical behaviors are investigated by the curves of equilibrium points, bifurcation diagram, Lyapunov exponents and phase trajectory diagrams. In order to verify the effectiveness and circuit realizability of linear augmentation control, based on the 3D four-wing system, a chaotic circuit is designed. The Multism simulation and hardware experimental results are in agreement with that of the MATLAB.