Control and identification of chaotic systems by altering their energy

We developed the control technique for (non)linear oscillators when repellors are stabilized by adjusting the system to energy levels corresponding to their stable counterparts. The technique does not require knowledge of the system equations. Two control strategies are possible. Following the first one, we simply test the systems by changing the feedback strength. This strategy does not require any computation of the control signal, and, hence, can be useful for control as well as identification of unknown systems. If the desired target can be identified (say, from the system time series), one can use another strategy based on goal-oriented control of the desired target. We analyze how the perturbation shape can be tuned so as to preserve the system natural response and discuss how to calculate the minimal strength of the perturbation required for stabilization of a priori chosen orbit. Generally, the control represents addition of an extra nonlinear damping to the system. In two limits of the perturbation slope, it manifests itself in (i) changing the oscillator natural damping; (ii) suppressing (enhancing) the external driving force. In the case of large deviations between phases of the chaotic oscillator and the driving force, only first scenario holds. Generalization of the technique to the case of oscillator networks and 3D autonomous dynamical systems is considered.