Predictive Feedback Control Method for Stabilization of Continuous Time Systems

Abstract

Recent researchers have studied the chaotic phenomenon and introduced methods to control chaos. One of these methods is the Predictive Feedback Control (PFC). PFC method has been used to stabilize only the discrete chaotic maps. In this paper, we generalize the PFC method by extending it to stabilize continuous time systems. The numerical simulations are carried out to solve the system using Euler method for its simplicity, and then the PFC method is applied to the discretized system. The controlled trajectory converges to an unstable equilibrium point via small control action. The stability analysis is shown compared to that of the continuous system in details. Also the choice of the controlling input of the PFC method and its properties are discussed. Lorenz system and R\"ossler system are the well known chosen chaotic examples. The PFC method is applied to each of them, showing stability at each of their equilibrium point. With a very small control, the behaviour of the system is completely changed from chaos to stable.