Chaos control in uncertain dynamical systems using nonlinear delayed feedback

In this paper based on the sliding mode concept, a nonlinear delayed feedback control is proposed for stabilizing the unstable periodic orbits (UPOs) of chaotic systems. It is assumed that the period of the desired UPO is known, but its time series and the initial conditions generated the UPO are not available. The ability of the proposed control method in stabilizing the UPO of the chaotic systems is analytically proved and the effectiveness of the method is numerically examined by applying it to the chaotic Duffing system.