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This article investigates the adaptive fuzzy prescribed time H ∞ congestion control problem for a class of high speed transmission control protocol/active queue management (HSTCP/AQM) systems subject to asymmetric input saturation and external disturbance. Firstly, a saturation-based finite-time performance function (SFTPF) is constructed by introducing a nonnegative modified signal associated with input saturation errors into user-defined performance boundaries, which features the capability of ensuring the user-appointed tracking performance when no saturation exists and degrading it once saturation occurs, thereby effectively increasing the flexibility and reliability of the control scheme. Then, by designing a novel shifting function, the condition that the initial value of the queue tracking error remains within that of SFTPF is relaxed, which avoids the SFTPF being redeveloped for different initial queue tracking errors. Thereafter, an auxiliary system and H ∞ control theory are employed to eliminate the adverse effect caused by input saturation and external disturbance, respectively. Moreover, through the Lyapunov stability analysis, it is proven that, under our proposed adaptive fuzzy congestion control scheme, all the closed-loop signals are bounded, and the connection between input saturation and performance-related constraint is established. Finally, a set of simulation results are presented to demonstrate the feasibility and effectiveness of the designed congestion controller. • A new shifting function is developed to relax the initial condition restriction. • An error transformation function is designed to solve asymmetric constrained issues. • The performance constraint boundaries can be resiliently enlarged and recovered. • An adaptive fuzzy practical prescribed time congestion control scheme is proposed. [ABSTRACT FROM AUTHOR]