Disturbance Observer Based Adaptive Control Scheme for Synchronization of Fractional Order Chaotic Systems With Input Delay

ABSTRACT In recent years, considerable attention has been attracted to the synchronization of chaotic systems due to their important applications. However, fractional order non‐linear chaotic systems face critical challenges, particularly from input delays and external disturbances in practical applications. In this paper, a robust synchronization method based on state prediction is introduced to address these challenges. First, a novel adaptive disturbance observer for fractional order systems is proposed, ensuring that disturbance estimation is achieved within an arbitrary time. The effects of disturbances are mitigated by this observer, which plays a crucial role in synchronization scheme design. Second, an arbitrary time exponential sliding mode controller that integrates state prediction and the disturbance observer is presented to handle input delay in fractional chaotic systems subjected to external disturbances. Third, a control scheme incorporating state prediction and sliding mode control is developed to address chaos synchronization for fractional systems with time varying input delays and disturbances. Additionally, an upper bound for input delay is established, demonstrating that if the delay remains below this threshold, the synchronization error is constrained. The efficacy and practical applicability of the proposed synchronization scheme are confirmed through simulation studies and experimental validation on a real‐time Speedgoat machine.