## Abstract and Applied Analysis

### Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 758176, 14 pages.

Dates
First available in Project Euclid: 3 October 2014

https://projecteuclid.org/euclid.aaa/1412364367

Digital Object Identifier
doi:10.1155/2014/758176

Mathematical Reviews number (MathSciNet)
MR3214450

Zentralblatt MATH identifier
07023026

#### Citation

Zhou, Wei-Dong; Liao, Cheng-Yi; Zheng, Lan. Adaptive Backstepping Control for a Class of Uncertain Nonaffine Nonlinear Time-Varying Delay Systems with Unknown Dead-Zone Nonlinearity. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 758176, 14 pages. doi:10.1155/2014/758176. https://projecteuclid.org/euclid.aaa/1412364367

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