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An adaptive nonlinear feedback-control method is proposed to control continuous-time chaotic dynamical systems,where the adaptive nonlinear controller acts on only one-dimensional error signals between the desired state and the observed chaotic state of a system. The reduced parameter adaptive quadratic predictor used in adaptive feedback cancellation of the nonlinear terms can control the system at any desired state. Computer simulation results on the Lorenz system are shown to demonstrate the effectiveness of this feedback-control method.