Robust Stochastic Predefined-Time Control and Its Application to Single-Link Robotic Arm Systems

This paper proposes a robust stochastic predefined-time control method for a single-link robotic arm system subject to stochastic disturbances and input saturation. To mitigate the effects of stochastic noise, external interference, and input saturation, an auxiliary variable system is designed to address the control input saturation issue. Based on the adaptive back-stepping procedure, virtual control laws, actual control laws, and adaptive parameter update laws are developed, while a fuzzy logic system is utilized to approximate unknown nonlinear functions. Finally, by employing predefined-time stability theory for stability analysis and simulation verification, the proposed method is shown to achieve precise tracking of the reference trajectory while maintaining smooth control inputs and overall system stability, thereby significantly enhancing the system’s robustness and control performance.