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This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection. [ABSTRACT FROM AUTHOR]