Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Input Saturation and External Disturbances

This study addresses the fixed-time tracking control of a class of uncertain strict-feedback nonlinear systems, where the nonlinear drift functions and external disturbances are unknown, while the control-gain functions are assumed to be known smooth functions with known signs and positive bounds. The systems are additionally subject to actuator saturation. A smooth hyperbolic-tangent model is employed to represent the saturation characteristic. On this basis, the mean-value theorem is utilized to obtain an equivalent input representation containing an unknown control effectiveness coefficient. The resulting saturation approximation error is incorporated with the external disturbance to construct a compound disturbance. In the backstepping framework, unknown nonlinearities are handled through fuzzy basis-function modeling, whereas adaptive mechanisms and smooth robust compensators are designed to mitigate the influence of approximation errors and lumped disturbances. A fixed-time command filter is introduced to eliminate the need for successive differentiation of virtual control laws, thereby reducing the computational complexity associated with conventional backstepping. Moreover, a bi-power compensator is introduced to reduce command-filter-induced errors while retaining fixed-time performance. The combined use of different-power feedback terms ensures practical fixed-time stability, with all closed-loop variables bounded and the tracking, compensation, and estimation errors driven into a prescribed neighborhood within an initial-condition-independent settling time. Simulations on a nonlinear damped car with symmetric/asymmetric saturation and time-varying disturbances confirm the tracking and disturbance-rejection performance of the proposed method.