Abstract-In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

Abstract-In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

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Abstract-Practical adaptive neural control is presented for a class of nonlinear systems with unknown time delays in strict-feedback form. Using appropriate Lyapunov-Krasovskii functionals, the unknown time delays are compensated for. Controller singularity problems are solved by practical neural network control. A novel differentiable control function is provided such that the practical design can be carried out in the decoupled backstepping design. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed-loop system, and the tracking error is proven to converge to a small neighborhood of the origin.Index Terms-Decoupled backstepping, differentiable control, nonlinear time-delay system, practical neural networks.

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