Stabilization of periodic orbits of discrete-time dynamical systems using the Prediction-Based Control: New control law and practical aspects

This paper tackles in the stabilization of periodic orbits of nonlinear discrete-time dynamical systems with chaotic sets. The problem is approximated locally to the stabilization of linear time-periodic systems and the theory of modern control is applied to the Prediction-Based Control, resulting in a new control law. This control law sets all the Floquet multipliers of the stabilized orbit to zero, resulting in fast convergence of trajectories in its vicinity. Another important characteristic of the control law is that no previous knowledge about the periodic orbit is required for stabilization. Using numerical simulations, this control law was analysed and compared to an optimal Delayed Feedback Control evidencing its advantages in theoretical and practical aspects.