四维Qi系统零平衡点的Hopf分岔反控制

通过线性与非线性状态反馈， 实现了对四维Qi系统零平衡点的Hopf分岔反控制.首先确定产生Hopf分岔的线性控制项，得到线性控制增益的选取原则.然后，利用稳定性分析，借助于对线性受控Qi系统的Jordan标准型的直接控制以及适当的变换，确定影响Hopf分岔稳定性的非线性控制项，得到非线性控制增益的选取原则.针对所考虑分岔参数的不同，给出不同的控制方案.最后通过数值模拟验证了理论分析结果的正确性. 关键词： Qi系统 Hopf分岔 反控制 稳定性

Anti-control of Hopf bifurcation at zero equilibrium of 4D Qi system

Anti-control of Hopf bifurcation at the zero equilibrium of the 4D Qi system is achieved by the linear and nonlinear state feedback. First, aimed at the emergence of the Hopf bifurcation, linear control terms are determined and the conditions which the linear control gains should satisfy are presented. Then, with respect to the nonlinear control terms, which are associated with the stability of Hopf bifurcation, the nonlinear feedback applied directly to the Jordan form of the Qi system is investigated. By the stability analysis and a proper transformation, the nonlinear control terms which play roles on the stability of Hopf bifurcation are collected and the condition restricting the nonlinear control gain isobtained. The control strategy is different as the bifurcation parameter concerned is altered. Finally, the numerical results are presented that confirm the analytical predictions.