Command filter approximator-based fixed-time fuzzy control for uncertain nonlinear systems with input saturation

This paper proposes a command filter approximator-based fixed-time fuzzy control (CFTFC) method for $n$-dimensional nonlinear systems subject to function uncertainties, input saturation, and external disturbances. Command filter approximators are designed to provide differential estimations for the $j$th $(j=1,2,\dots ,n-1)$ subsystem of the error system, addressing both function uncertainties and the complex explosive problem (CEP). Additionally, a single fuzzy logic system approximator is designed to approximate the unknown composite function, which includes the $n$th function uncertainty, the derivative of the $(n-1)$th virtual controller, and other system signals. Moreover, a smooth function is used to estimate the non-smooth input saturation. Based on these considerations, a fuzzy adaptive fixed-time controller is then designed. Rigorous theoretical analysis shows that all error signals converge to a neighborhood of the origin within a fixed time, regardless of the initial system states. Finally, comparative simulation experiments verify the effectiveness of the proposed controller.