In this paper we address the problem of controlling chaos by using a selective filter inserted in a negative feedback loop. This has been achieved in driven double-well Duffing oscillator in a parameter region exhibiting both a boundary crisis and generalized bistability. The optimization of the filter response allows us to improve the reduction of the control signal when the periodic solution competing with the chaotic attractor is approached. The advantage in using a selective frequency approach with respect to the Pyragas's method mainly resides in the tunability of the maximum of its amplitude response and zero phase condition. Numerical simulations performed in the temporal domain match with the experiment and make us glimpse the potential of an automatic adaptive strategy adopting filter parameter variations in order to reach an optimal feedback signal reduction.

中文翻译：

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演示边界危机附近的过滤反馈控制


在本文中，我们通过使用插入负反馈环路的选择性滤波器来解决控制混沌的问题。这已经在呈现边界危机和广义双稳态的参数区域中的驱动双阱杜芬振荡器中实现。滤波器响应的优化使我们能够在接近与混沌吸引子竞争的周期解时改善控制信号的减少。相对于 Pyragas 方法，使用选择性频率方法的优点主要在于其幅度响应最大值和零相位条件的可调谐性。在时域中进行的数值模拟与实验相匹配，使我们看到了采用滤波器参数变化的自动自适应策略的潜力，以达到最佳的反馈信号减少。