Exponential Optimal Synchronization of Chaotic Cryptosystems: Neural-Network-Based Approach

This paper presents a systematic design methodology for neural-network (NN) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H^∞ performance and cryptography. First, we use the n-shift cipher and key to the original message of transmission for encryption. The encrypted message is re-encrypted by using chaotic synchronization. A robust model-based fuzzy control design is then presented to address the effects of modeling errors between the MTDC systems and the NN models. Next, a delay-dependent exponential stability criterion is derived in terms of Lyapunov´s direct method to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into linear matrix inequalities (LMIs). According to the LMIs, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H^∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key.