Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication

This paper deals with the issues of chaotic synchronization and chaos-based secure communication for chaotic systems subject to uncertain parameters and channel disturbance. First, an augmented singular system is constructed by introducing an augmented vector which consists of both the state and channel disturbance vectors of original drive system, and a singular reduced-order observer which can not only synchronize the drive system but also reconstruct channel disturbance is developed for the augmented singular system. Second, a second-order sliding mode observer is considered to get the exact estimates of output derivatives in a finite time. Based on the estimates of states and output derivatives, a kind of algebraic unknown information recovery method which can recover information signal injected into the drive system and estimate parameter disturbance is proposed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.