A new adaptive fixed-time feedback control scheme for synchronization of uncertain chaotic systems with application to secure communication

Fixed-time synchronization control (FTSC) is essential for synchronizing chaotic systems within a guaranteed settling time independent of initial conditions, a critical requirement for real-time applications that demand predictability and precision. However, existing FTSC schemes often exhibit chattering, slow convergence of synchronization errors, and excessive energy consumption. Chattering mitigation is therefore crucial, as it prevents actuator wear, reduces energy waste, and enhances system reliability and longevity in practical implementations. To address these challenges, this paper proposes a novel adaptive fixed-time feedback synchronization control (AFTSC) scheme for uncertain master–slave chaotic systems. The proposed AFTSC employs a smooth continuous feedback structure that suppresses chattering, accelerates synchronization error convergence, and significantly reduces the time required for energy dissipation. Rigorous Lyapunov-based analysis establishes fixed-time convergence and closed-loop robustness in the presence of parametric uncertainties. The effectiveness of the proposed scheme is demonstrated through numerical simulations on two benchmark chaotic systems: the uncertain Shimizu-Morioka system and the uncertain Lorenz system. The results demonstrate a 70% improvement in synchronization speed and a 74% reduction in energy dissipation time compared with reference methods. Furthermore, the practical applicability of the proposed method is illustrated through a secure communication framework for the encryption and decryption of one-dimensional and two-dimensional images. These results confirm that the proposed AFTSC strategy is a robust, time- and energy-efficient solution for secure communication and real-time control of complex chaotic systems. Future work will extend the proposed framework to complex networks and multi-agent systems under higher levels of uncertainty.