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Mathematical Problems in Engineering
Volume 2017, Article ID 8084529, 9 pages
https://doi.org/10.1155/2017/8084529
Research Article

Adaptive Stabilization of Stochastic Nonlinear Systems Disturbed by Unknown Time Delay and Covariance Noise

1School of Electrical Engineering & Automation, Jiangsu Normal University, Xuzhou 221116, China
2School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
3School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China

Correspondence should be addressed to Na Duan; moc.361@80annaud

Received 6 March 2017; Accepted 2 April 2017; Published 30 April 2017

Academic Editor: Weihai Zhang

Copyright © 2017 Na Duan et al. 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.

Abstract

This paper considers a more general stochastic nonlinear time-delay system driven by unknown covariance noise and investigates its adaptive state-feedback control problem. As a remarkable feature, the growth assumptions imposed on delay-dependent nonlinear terms are removed. Then, with the help of Lyapunov-Krasovskii functionals and adaptive backstepping technique, an adaptive state-feedback controller is constructed by overcoming the negative effects brought by unknown time delay and covariance noise. Based on the designed controller, the closed-loop system can be guaranteed to be globally asymptotically stable (GAS) in probability. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.