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2014 Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity
Wei-Dong Zhou, Cheng-Yi Liao, Lan Zheng
Abstr. Appl. Anal. 2014(SI70): 1-14 (2014). DOI: 10.1155/2014/758176

Abstract

An adaptive backstepping controller is constructed for a class of nonaffine nonlinear time-varying delay systems in strict feedback form with unknown dead zone and unknown control directions. To simplify controller design, nonaffine system is first transformed into an affine system by using mean value theorem and the unknown nonsymmetric dead-zone nonlinearity is treated as a combination of a linear term and a bounded disturbance-like term. Owing to the universal approximation property, fuzzy logic systems (FLSs) are employed to approximate the uncertain nonlinear part in controller design process. By introducing Nussbaum-type function, the a priori knowledge of the control gains signs is not required. By constructing appropriate Lyapunov-Krasovskii functionals, the effect of time-varying delay is compensated. Theoretically, it is proved that this scheme can guarantee that all signals in closed-loop system are semiglobally uniformly ultimately bounded (SUUB) and the tracking error converges to a small neighbourhood of the origin. Finally, the simulation results validate the effectiveness of the proposed scheme.

Citation

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Wei-Dong Zhou. Cheng-Yi Liao. Lan Zheng. "Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity." Abstr. Appl. Anal. 2014 (SI70) 1 - 14, 2014. https://doi.org/10.1155/2014/758176

Information

Published: 2014
First available in Project Euclid: 3 October 2014

zbMATH: 07023026
MathSciNet: MR3214450
Digital Object Identifier: 10.1155/2014/758176

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI70 • 2014
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