In this chapter, considering a class of nonlinear systems with full state constraints and actuator faults, an adaptive neural network output-feedback fault-tolerant control algorithm with prescribed performance is proposed. A state observer is constructed to solve the unmeasurable states problem. Unknown nonlinear functions in the systems are approximated by radial basis function neural networks (RBF NNs). By introducing the nonlinear mapping, the systems with state constraints are transformed into novel systems without state constraints. Moreover, a novel performance function is utilized to guarantee that the tracking error converges within a preset time. Meanwhile, the convergence speed can be adjusted through the parameter design. Finally, it is proved that the control algorithm ensures that all signals in the closed-loop systems are semi-globally uniformly ultimately bounded. The effectiveness of the algorithm is verified by a numerical simulation.