Improved Adaptive Stabilization Controller for an UPOs of Chaotic Systems‎~ ‎with an Optimal Principle by TDFC Method

‎In this paper‎, ‎we investigate an improved method for stabilizing a class of uncertain chaotic nonlinear dynamical system‎. ‎Our approach follows techniques of optimal principle for time-delayed feedback control and adaptive tracking control theory for stabilizing unstable periodic orbits in a chaotic bounded attractor‎. ‎The uncertain parameters expressed in the system can be separated‎. ‎Analysis and proof are presented using the Lyapunov stability theorem‎. ‎In particular‎, ‎we use the adaptive control theory to design an adaptive law for the estimation of uncertain time-delayed controlled chaotic nonlinear dynamical systems‎. ‎The predictions are presented by numerical simulation through the Rossler system to demonstrate theoretical results‎.