Adaptive neural synchronization control of chaotic systems with unknown control directions under input saturation

In this paper, we investigate the synchronization problem of chaotic systems with unknown control direction under input saturation nonlinearity. By utilizing backstepping technique, an adaptive neural synchronization control scheme is developed via neural approximation technique and Nussbaum-type function method. To deal with the problem of sharp corner of saturation, a tangent function based smooth function is used to approximate input saturation. To facilitate controller design, an auxiliary signal is constructed to augment the plant. Two Nussbaum functions are respectively used to deal with unknown control direction and compensate for the time-varying gain arising from the partial differentiation of the smooth function of input saturation. Tracking-differentiator is introduced to handle the problem of “explosion of computation” in the backstepping design. Adaptive robust effects are designed to deal with the “disturbance-like” term and tracking-differentiator estimation error. Lyapunov based analysis gives the transient performance and convergence of synchronization errors. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.