Control of time-delayed feedback systems with application to optics

We have investigated a new control scheme of chaotic orbit for time-delayed feedback systems and have applied this method to an optical system in which the nonlinear function is the so-called 'Ikeda function'. Discrete time evolution characterizes the delay-differential equation modelling the system for a large enough delay. We use this discrete map to design the control process and we show that stabilized orbits are closed to stable orbits of the original system; moreover, the control signal is built upon real-time trajectories out of the chaotic's system evolution. Analytical predictions are in good agreement with simulations and the experimental results are obtained.