Fuzzy control for exponential H^∞ synchronization of chaotic cryptosystems using an Improved Genetic Algorithm

This paper presents a systematic design methodology for neural-network 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. 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. On the basis of the Improved Genetic Algorithm, which is demonstrated to have better performance than that of a traditional Genetic Algorithm, 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.