Fixed-time saturated synchronization of a class of fractional-order chaotic systems with disturbances

This paper addresses the saturated synchronization problem for a class of fractional-order chaotic systems under external disturbances. Unlike studies focused on single system models, we establish an analytical framework for a representative family of chaotic systems, enhancing the generality and applicability of the results. A key contribution is the development of a novel backstepping-based saturated control scheme that achieves effective synchronization using only a single controller. This overcomes the limitation of traditional approaches, which typically require multiple independent controllers (e.g., three). This breakthrough substantially reduces the complexity of the control structure, the number of required components, and the demand for computational resources while maintaining performance, demonstrating the scheme's efficiency and engineering practicality. Crucially, the controller design explicitly and simultaneously incorporates both the ubiquitous physical constraint of actuator saturation and the influence of external bounded disturbances, which model environmental uncertainties. By rigorously accounting for these critical practical factors, the proposed control law ensures not only theoretical feasibility but also enhanced robustness and adaptability in real-world operating environments. Numerical validation on the Fractional-Order Genesio-Tesi chaotic system confirms the method's efficacy and physical feasibility.