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In this paper, an adaptive dynamic sliding-mode control system (ADSMCS) with recurrent radial basis function network (RRBFN) for indirect field-orientation control induction motor (IM) drive is proposed. The ADSMCS comprises a dynamic sliding-mode controller (DSMC), an RRBFN uncertainty observer and a robust controller. The DSMC is proposed to reduce the chattering phenomenon. However, due to the uncertainty bound being unknown of the switching function for the DSMC, an ADSMCS is proposed to increase the robustness and improve the control performance of IM drive. In the ADSMCS, an RRBFN uncertainty observer is used to estimate an unknown nonlinear time-varying function of lumped parameter uncertainty online. Moreover, the adaptive learning algorithms for the RRBFN are derived using the Lyapunov stability theorem to train the parameters of the RRBFN online. Furthermore, a robust controller is proposed to confront the uncertainties including approximation error, optimal parameter vector and higher order term in Taylor series. A computer simulation and an experimental system are developed to validate the effectiveness of the proposed ADSMCS. All control algorithms are implemented in a TMS320C31 DSP-based control computer. The simulation and experimental results confirm that the ADSMCS grants robust performance and precise response regardless of load disturbances and IM uncertainties.