Fixed-time robust synchronous control for the double-lift system of the overhead crane via adaptive reinforcement learning with prescribed performance

Precise synchronous control of the double-lift overhead crane system is challenging due to inherent strong coupling, parameter variations, and complex uncertain disturbances. While existing model-based approaches rely heavily on precise system dynamics, which are difficult to obtain in practice, conventional model-free methods often suffer from slow convergence rates and cannot explicitly constrain transient tracking and synchronization errors. These limitations can lead to excessive overshoot or synchronization deviations, posing potential safety risks such as mechanical tearing or collision between spreaders. To address these specific demerits, this paper develops a new model-free synchronous control method integrating prescribed performance control, reinforcement learning, and fixed-time sliding mode control. First, prescribed performance control is employed to guarantee both transient and steady-state response characteristics while maintaining state constraints. Second, an identifier–critic reinforcement learning scheme is introduced to estimate system uncertainties. The neural network–based identifier learns the uncertain nonlinear dynamics, while the critic network approximates solutions to the Hamilton–Jacobi–Bellman equation, reducing computational complexity compared with conventional actor–critic frameworks. Furthermore, by incorporating experience replay technology into the critic, a novel weight update rule is developed to enhance learning efficiency. Then, a new fixed-time sliding mode controller is designed to accelerate state convergence, with compensation for the neural network estimation errors. Finally, utilizing fixed-time convergence concepts and Lyapunov stability theory, we analytically prove the system stability, guaranteeing a fixed settling time independent of initial states, which distinguishes this work from conventional finite-time reinforcement learning schemes. Simulation results confirm the efficacy of the synchronous control scheme. Specifically, compared with the standalone prescribed performance control and RBF neural network sliding mode control (RBF-SMC) methods, the proposed controller reduces the root mean square error by 86.5% and 76.2%, respectively. Furthermore, the system tracking error convergence time is shortened by 42.6% and 55.7%, respectively, ensuring rapid and precise synchronization under uncertain disturbances in the interlocked mode.