No-chatter model-free sliding mode control for synchronization of chaotic fractional-order systems with application in image encryption

Synchronization of different Chaotic dynamical systems is one of the main issues in engineering which has a lot of applications in applied sciences like secure communications and cryptography. In this work, a chattering-free fractional-integral-based sliding mode control (SMC) methodology is proposed for the synchronization of different chaotic fractional-order systems with input saturation. Based on the frequency distributed model and the non-integer version of the Lyapunov stability theorem and using a new continuous function instead of sign function, a novel model-free SMC (MFSMC) method is proposed to overcome the chaotic behavior of the FOSs without any undesired chattering phenomenon. In addition, utilizing the boundedness property of the fractional-order chaotic system is caused to design the method. Then, by operating the proposed scheme on chaotic fractional-order systems, which are applied in electrical systems and secure communications, the effectiveness and applicability of the MFSMC are validated. After that, to show the real-world application, a novel encryption/decryption method for color images is introduced based on the proposed MFSMC. According to an adaption of the pre-diffusion-permutation-diffusion, the structure is adopted to improve the level of security. Furthermore, the performance and security analyses are given to confirm the superiority of the proposed encryption scheme, including histogram analysis, adjacent pixel correlation analysis, and information entropy analysis.