Directing nonlinear dynamic systems to any desired orbit

A method of controlling arbitrary nonlinear dynamic systems, dx/dt=F(x,t) (x∈[formula presented] ), is presented. It is proved that the system can be entrained to any arbitrary 'goal' dynamics g(t) by use of the open-loop action and adjusting the control parameter at the same time. Examples of some entrainment 'goals' are given for the Lorenz and the Rössler systems. The basins of entrainment are also established for the Lorenz, Rössler, and Duffing systems. Numerical studies show that this method works as well as the closed-loop control method [Physica D 85, 1 (1995); Phys. Lett. A 213, 148 (1996)].