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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 238018, 14 pages
Research Article

A New AILC for a Class of Nonlinearly Parameterized Systems with Unknown Delays and Input Dead-Zone

Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China

Received 23 March 2014; Revised 12 May 2014; Accepted 26 May 2014; Published 24 June 2014

Academic Editor: Bin Zhou

Copyright © 2014 Jian-ming Wei 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.


This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of deadzone nonlinearity is presented. The assumption of identical initial condition for ILC is removed by introducing boundary layer functions. The uncertainties with time-varying delays are compensated for with assistance of appropriate Lyapunov-Krasovskii functional and Young’s inequality. The hyperbolic tangent function is employed to avoid the possible singularity problem. According to a property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while maintaining all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.