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In this paper, a mixed controller for solving the trajectory tracking and point stabilization problems of a mobile robot is presented, applying the integration of backstepping technique and neural dynamics. By introducing a virtual target point, the whole motion process is divided into two parts. The first one is employed to realize tracking control and the other one is adopted to implement point stabilization. Each part produces a feedback control law by using backstepping technique. Moreover, to solve the speed and torque jump problems and make the controller generate smooth and continuous signal when controllers switch, the neural dynamics model is integrated into the backstepping. The stability of the proposed control system is analyzed by using Lyapunov theory. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.