Design of a model-free adaptive sliding mode control to synchronize chaotic fractional-order systems with input saturation: An application in secure communications

Abstract

In this work, a model-free adaptive sliding mode control (ASMC) methodology is proposed for synchronization of chaotic fractional-order systems (FOSs) with input saturation. Based on the frequency distributed model and the non-integer version of the Lyapunov stability theorem, a model-free ASMC method is designed to overcome the chaotic behavior of the FOSs. The control inputs are free from the nonlinear-linear dynamical terms of the system because of utilizing the boundedness feature of the states of chaotic FOSs. Moreover, a new medical image encryption scheme is tentatively proposed according to our synchronization method, and its effectiveness is verified by numerical simulations. Furthermore, the performance and security analyses are given to confirm the superiority of the proposed encryption scheme, including statistical analysis, key space analysis, differential attack analysis, and time performance analysis.