A nonlinear open-plus-closed-loop (NOPCL) control strategy is proposed in this paper to entrain complex dynamic systems to arbitrarily given goal dynamics. It contains nonlinear closed-loop control actions as well as nonlinear open-loop control actions. Compared to the existing open-plus-closed-loop (OPCL control, the NOPCL control usually results in much simpler error equations that determine the basins of entrainment of the controlled dynamic systems. For a large number of dynamic systems such as the Lorenz, Rossler, Duffing, Van der Pol, and Chua systems, the NOPCL control is shown to have global basins of entrainment for arbitrarily given goal dynamics
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