Extended resonant feedback technique for controlling unstable periodic orbits of chaotic system

An improvement of the recently described resonant chaos control method is suggested. Negative feedback loop containing a notch-rejection filter, tuned to the main harmonic of the unstable periodic orbit, is supplemented with a set of notch filters tuned to the higher harmonics. The extended method is applied to an electrical circuit representing the Duffing–Holmes type non-autonomous two-well chaotic oscillator. Stabilization of the period-1 orbit is achieved with very small control force. The residual control signal is about 1% compared to the main variable. Mathematical model based on a two-well piecewise parabolic potential is presented and numerical simulation is performed. Numerical results are confirmed by hardware experiments.