Observer-Based Synchronization of Chaotic Systems with Both Parameter Uncertainties and Channel Noise

This paper considers observer-based chaos synchronization and chaos-based secure communication problems for a class of uncertain chaotic systems with both parameter uncertainties and channel noise. First, by introducing an augmented vector, the original system is transformed into a new system which has no channel noise. Second, based on the concept of relative degree, an auxiliary drive signal vector is constructed so that the observer matching condition is satisfied. Third, a reduced-order observer is designed to estimate the states of the new augmented system. Then, a high-order high-gain sliding mode observer is considered to estimate the auxiliary drive signals and their derivatives exactly in a finite time. After this, the combination of the reduced-order observer and the high-order high-gain sliding mode observer is used as the receiver in the secure communication mechanism. And a kind of secure information recovery method is developed. Finally, a four-dimensional hyperchaos system is used as the simulation example to illustrate the effectiveness of the proposed methods.