Practical Fixed-Time Tracking Control for Nonlinear High-Order Fully Actuated System with Unknown Control Coefficients

This paper addresses the practical fixed-time (FxT) tracking control for nonlinear high-order fully actuated (HOFA) systems with unknown control coefficients and nonlinear dynamics. First, an adaptive compensation law is designed by integrating neural network approximation with adaptive techniques, incorporating both negative low-order and high-order terms to effectively compensate for the system's unknown nonlinearities within a fixed time. Based on fully actuated system (FAS) theory, an adaptive FxT tracking controller is then developed, incorporating the Nussbaum gain function and intermediate control variables to manage the impact of unknown control coefficients on system stability. Specifically, the intermediate control variables include negative fractional-order terms of the tracking error to promote FxT convergence of the closed-loop system. Using FxT stability analysis theory, it is rigorously proven that the controller ensures practical fixed-time convergence of the closed-loop system. Finally, the effectiveness of the proposed control scheme is validated through simulations of a pendulum system model.