Universal control approach for high dimensional chaotic systems within a region of attraction

a universal approach for controlling high dimensional chaotic systems is proposed, in which the controllability assumption can be relaxed and only the stabilization condition is required. Meanwhile, estimation the region of attraction of a desired embedded orbit on the map is evaluated, to shorten the tedious waiting time of acting the controller. The main feature of the proposed method is that all of the controllable unstable eigenvalues of the linear approximation assigned to be zero; the stable eigenvalues that remain may be uncontrollable. Only small parameter perturbations are required to stabilize chaotic situation when the trajectory falls in the neighborhood of the desired fixed point, the region of attraction of a stabilized embedded orbits. Simulations will carry out for verifying the study.