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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 529862, 13 pages
Research Article

Adaptive Neural Output Feedback Control of Stochastic Nonlinear Systems with Unmodeled Dynamics

Department of Automation, College of Information Engineering, Yangzhou University, Yangzhou 225127, China

Received 9 April 2014; Revised 17 June 2014; Accepted 4 July 2014

Academic Editor: Ming Gao

Copyright © 2015 Xiaonan Xia and Tianping Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states. The unmeasured states are estimated by K-filters, and unmodeled dynamics is dealt with by introducing a novel description based on Lyapunov function. The neural networks weight vector used to approximate the black box function is adjusted online. The unknown nonlinear system functions are handled together with some functions resulting from theoretical deduction, and such method effectively reduces the number of adaptive tuning parameters. Using dynamic surface control (DSC) technique, Itô formula, and Chebyshev’s inequality, the designed controller can guarantee that all the signals in the closed-loop system are bounded in probability, and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results are provided to verify the effectiveness of the proposed approach.