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In this paper, an adaptive dynamic programming-based online adaptive tracking control algorithm is proposed to solve the tracking problem of the partial uncertain time-delayed nonlinear affine system with uncertain resistance. Using the discrete-time Hamilton-Jacobi-Bellman function, the input time-delay separation lemma, and the Lyapunov-Krasovskii functionals, the partial state and input time delay can be determined. With the approximation of the action and critic, and resistance neural networks, a near-optimal controller and appropriate adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the target system, and the tracking error convergence to a small compact set to zero. A numerical simulation of the wheeled mobile robotic system is presented to verify the validity of the proposed method.
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Li et al. (2019) studied this question.
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