tIn this paper, we investigate the

tIn this paper, we investigate the synchronization problem of chaotic systems with unknowncontrol direction under input saturation nonlinearity. By utilizing backstepping technique,an adaptive neural synchronization control scheme is developed via neural approximationtechnique and Nussbaum-type function method. To deal with the problem of sharp cor-ner of saturation, a tangent function based smooth function is used to approximate inputsaturation. To facilitate controller design, an auxiliary signal is constructed to augment theplant. Two Nussbaum functions are respectively used to deal with unknown control direc-tion and compensate for the time-varying gain arising from the partial differentiation ofthe smooth function of input saturation. Tracking-differentiator is introduced to handlethe problem of “explosion of computation” in the backstepping design. Adaptive robusteffects are designed to deal with the “disturbance-like” term and tracking-differentiatorestimation error. Lyapunov based analysis gives the transient performance and conver-gence of synchronization errors. Finally, a simulation example is presented to verify theeffectiveness of the proposed approach.