I do not know what I may appear to the world, bu.t to myself I seem to have been only like a boy playing on the seashore, diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, while the great ocean of truth lay all u.ndiscovered before me.

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This paper presents a novel control method for a general class of nonlinear systems using neural networks (NNs). Firstly, under the conditions of the system output and its time derivatives being available for feedback, an adaptive state feedback NN controller is developed. When only the output is measurable, by using a high-gain observer to estimate the derivatives of the system output, an adaptive output feedback NN controller is proposed. The closed-loop system is proven to be semi-globally uniformly ultimately bounded (SGUUB). In addition, if the approximation accuracy of the neural networks is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussions.

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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