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This paper aims to solve the path following problem for an underactuated unmanned-surface-vessel (USV) based on deep reinforcement learning (DRL). A smoothly-convergent DRL (SCDRL) method is proposed based on the deep Q network (DQN) and reinforcement learning. In this new method, an improved DQN structure was developed as a decision-making network to reduce the complexity of the control law for the path following of a three-degree of freedom USV model. An exploring function was proposed based on the adaptive gradient descent to extract the training knowledge for the DQN from the empirical data. In addition, a new reward function was designed to evaluate the output decisions of the DQN, and hence, to reinforce the decision-making network in controlling the USV path following. Numerical simulations were conducted to evaluate the performance of the proposed method. The analysis results …