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IEEE Trans Syst Man Cybern B Cybern. 2010 Jun;40(3):939-50. doi: 10.1109/TSMCB.2009.2033808. Epub 2009 Nov 24.

Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays.

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Department of Applied Mathematics and the Key Laboratory of Intelligent Perception and Image Understanding, Ministry of Education of China, Xidian University, Xi'an 710071, China.


For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.

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