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This paper considers chaos synchronization and chaos-based secure communication problems based on high-gain sliding mode unknown input observers when the observer matching condition is not satisfied to the drive signal. An auxiliary drive signal vector which satisfies the observer matching condition is introduced and an adaptive and robust observer is developed by using the auxiliary drive signal directly to not only estimate the states but also adjust adaptively the unknown parameters and the Lipschitz constants of the nonlinear terms. A high-gain sliding mode observer is considered to exactly estimate both the auxiliary drive signals and their derivatives in a finite time only based on the original drive signal. The combination of the adaptive and robust observer and the high-gain sliding mode observer becomes the receiver in chaos-based secure communication discussion. A kind of information signal recovering method is developed based on both the state synchronization and exact estimates of the derivatives of the auxiliary drive signals. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.