We present a dynamical control method where a trajectory on a chaotic attractor is directed by small perturbations towards a chosen unstable set. This method is alternative to the classical OttGrebogi- Yorke control procedure. Our approach is based on the discrete and continuous maximum principles and optimizes the mean time to achieve control even at large distances from the desired state. The proposed method is tested both in simple models (one-dimensional and two-dimensional maps) and in multidimensional systems (complex Ginzburg-Landau equations). A possible decrease of the strange attractor dimension by means of this method is also discussed.
Keywords: controlling chaos, optimal control, strange attractor, multistep algorithms