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To begin with, with the aim to improve convergence speed and tracking precision, a novel complementary terminal sliding mode surface (NCTSMS) is developed. Then, a specific cost function related to the NCTSMS is developed, and the initial control problem is then transformed toward a series of optimal control problems. The Hamilton-Jacobi-Bellman (HJB) problem is then solved by a single critic neural network, yielding the estimated optimal controller. Finally, using the finite-time lemma, we design a Lyapunov function and verify the system\u2019s fast finite-time convergence. 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