Demonstrating Filtered Feedback Control Near a Boundary Crisis

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.