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In this paper, a trajectory tracking control for a nonholonomic mobile robot by the integration of a kinematic controller and neural dynamic controller is investigated, where the wheel actuator (e.g., dc motor) dynamics is integrated with mobile robot dynamics and kinematics so that the actuator input voltages are the control inputs. The proposed neural dynamic controller (PNDC), based on the sliding mode theory, is applied to compensate the mobile robot dynamics, bounded unknown disturbances, and influence of payload. This controller is obtained by modeling the Radial Basis Functions Neural Networks (RBFNNs) of the centripetal and Coriolis matrix through of the inertia matrix of the mobile robot dynamics. Thus, PNDC is constituted of static RBFNNs only, what makes possible the reduction of the size of the RBFNNs, of the computational load and the implementation in real time. Stability analysis and numerical simulations are provided to show the effectiveness of the PNDC.