Adaptive Fixed-Time Control for High-Order Fully Actuated System with Input Saturation

This paper studies the fixed-time (FxT) tracking control problem of an uncertain high-order fully actuated (HOFA) system with parameter uncertainty, external disturbance, and input saturation. Firstly, to tackle the impact of the input saturation on the system, a hyperbolic tangent function is introduced to approximate the saturation function. Subsequently, utilizing the HOFA system method, an intermediate control variable with adaptive laws and a tracking error fractional order term is designed, which can effectively compensate for system parameter uncertainty and external disturbances, while promoting the FxT stability of the system. Based on this, a FxT controller is then constructed, incorporating an adaptive law designed to effectively manage the uncertainty in the input matrix resulting from the estimation of the saturation function. By employing FxT stability theory, the designed adaptive controller guarantees the boundedness of all system states, while ensuring that the tracking error converges to a small neighborhood of the origin within a fixed time. Finally, the effectiveness of the proposed control scheme is verified by simulating a three degree of freedom marine surface vessel system model.