In this paper, the problem of adaptive tracking control for a class of uncertain switched nonlinear systems is studied. The uncertain nonlinear functions in the system model are approximated using radial basis function neural network, and the unmeasured states under asynchronous switching and actuator faults are estimated by designing a time-schedule state observer. Further, adaptive laws subject to delta function are designed to make adaptive parameters continuous during persistent switching. It is proved that under asynchronous switching, the closed-loop system is stable with tracking error converging to a small neighborhood of origin. Finally, an example of a continuous stirred tank reactor is studied to verify the effectiveness of the approach proposed in this paper.