Feedback control of probability amplitudes for two-level atom in optical field

We demonstrate the possibility to stabilize the probability amplitude of the upper level for a single quantum two-level atom in a classical optical field with feedback control scheme.Comment: 7 pages, 3 figure

Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.Comment: 7 pages, 6 figure

Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay or various cluster states, can be selected.Comment: 8 pages, 7 figure