An open-loop trajectory planning algorithm is presented for computing an input sequence that drives an input-output system such that a reference trajectory is tracked. The algorithm utilizes only input-output data from the system to determine the proper control sequence, and does not require a mathematical or identified description of the system dynamics. From the input-output data, the controlled input trajectory is calculated in a ''one-step-ahead'' fashion using local modeling. Since the algorithm is calculated in this fashion, the output trajectories to be tracked can be nonperiodic. The algorithm is applied to a driven Lorenz system, and an experimental electrical circuit and the results are analyzed. Issues of stability associated with the implemen- tation of this open-loop scheme are also examined using an analytic example of a driven Henon map, problems associated with inverse controllers are illustrated, and solutions to these problems are proposed. @S1063-651X~97!02709-8# Numerous methods for the control of nonlinear systems have been developed recently. In the control community, some of the more popular methods include geometric control methods based on methods from differential geometry ~see Ref. @1# for an introduction!, nonlinear model predictive con- trol @2#, and control based on neural networks @3#. In order to use these methods for control, it is necessary to have an accurate description of the system dynamics. This model can be the result of physical knowledge of the system dynamics or the result of system identification. While these methods are popular in the literature of the control community, differ- ent methods of control have been pursued for the control of chaotic systems. Recently published methods of control for chaotic sys- tems also build controllers based on a knowledge of the sys- tem dynamics. However, most of these methods rely on a knowledge of the underlying dynamics of the undriven, au- tonomous system @4-6#. The chaotic system is then stabi- lized around an unstable periodic orbit or fixed point using proportional linear feedback control. In the method of Ott, Grebogi, and Yorke ~OGY !@ 4 #, and a number of later modi- fications, a scalar-controlled input is changed at discrete times such that a periodic orbit or fixed point of the system becomes stable. The implementation of the OGY algorithm requires knowledge of the linearized dynamics of the peri- odic orbit to be stabilized ~a fixed point on the Poincare ´