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.