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.

在这项工作中，提出了一种无模型自适应滑模控制 (ASMC) 方法，用于同步具有输入饱和的混沌分数阶系统 (FOS)。基于频率分布模型和非整数版本的李雅普诺夫稳定性定理，设计了一种无模型的 ASMC 方法来克服 FOS 的混沌行为。由于利用了混沌 FOS 状态的有界特征，控制输入不受系统的非线性-线性动力学项的影响。此外，根据我们的同步方法，初步提出了一种新的医学图像加密方案，并通过数值模拟验证了其有效性。此外，还给出了性能和安全性分析，以确认所提出的加密方案的优越性，包括统计分析、