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Mobile robots have been one of the challenging topics of control due to their nonholonomic property and restricted mobility. This paper presents the design of a novel tracking controller for a mobile robot by integrating the neural dynamics model into a conventional feedback controller. The proposed controller is capable of generating real-time smooth velocities, and driving the mobile robot to track desired trajectories. It resolves the speed jump problem existing in some previous tracking controllers. Lyapunov stability theory is used to prove the stability of the control system and the convergence of tracking errors to zero. The effectiveness of the proposed controller is demonstrated by simulation and comparison studies.