A polynomial-fuzzy-model-based synchronization methodology for the multi-scroll Chen chaotic secure communication system

Abstract In this paper, a polynomial-fuzzy-model-based design methodology to synchronize multi-scroll Chen chaotic systems is proposed for secure communication. At first, the architecture of secure communication system (SCS) based on the synchronization of multi-scroll Chen chaotic systems is presented. Then, the master and slave multi-scroll Chen chaotic systems are transformed into the equivalent master and slave polynomial fuzzy models respectively. After that, the H ∞ polynomial fuzzy control design is proposed for synchronizing the master and slave multi-scroll Chen chaotic systems as well as restraining external disturbances. Moreover, for practical application, a constraint on the control input is also considered. The H ∞ polynomial fuzzy control design is represented in terms of sum-of-squares (SOS) conditions which can be efficiently solved by the polynomial optimization Matlab toolbox SOSOPT. Furthermore, simulation results show the effectiveness of the proposed polynomial-fuzzy-model-based control design methodology. After the control design, the polynomial-fuzzy-model-based chaotic synchronization methodology is applied to implement the SCS. Finally, three experiments are given to demonstrate the practicality of the implemented SCS.