Practical Fixed-Time Tracking Control for a Class of Strict-Feedback Nonlinear Systems: A Fixed-Time Disturbance Observer Approach.

This article develops a practical fixed-time tracking control framework for a class of strict-feedback nonlinear systems subject to unknown external disturbances. A fixed-time disturbance observer (FxTDO) is first designed to reconstruct the disturbances together with their higher-order derivatives within a uniform settling time whose upper bound is independent of the initial conditions. To avoid the explosion of complexity arising from the repeated differentiation of virtual controllers, a fixed-time command filter (FxTCF) is incorporated into the recursive backstepping design. In contrast to conventional command filters with persistent filtering errors, the proposed FxTCF guarantees that the filtering error vanishes within a fixed time. A switching function is further embedded into the virtual control laws to ensure the required second-order differentiability and enable the effective implementation of the FxTCF without introducing additional error compensation dynamics. Moreover, a dynamic event-triggering mechanism is integrated into the control framework to reduce unnecessary transmissions while preserving the desired closed-loop performance. Theoretical analysis establishes the boundedness of all closed-loop signals, the practical fixed-time convergence of the tracking error to a prescribed residual set, and the exclusion of Zeno behavior. Simulation results for a flexible robotic manipulator demonstrate the effectiveness and advantages of the proposed control framework.