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

Jian-ming Wei,Mei-mei Sun,Yun-an Hu

doi:10.1155/2014/238018

Abstract

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.

Highlights

Many engineering systems carry out repetitive tasks in fixed finite space, such as manipulators [1,2,3]
This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown timevarying delays and unknown input dead-zone
One of the most important developments is adaptive ILC (AILC) [13,14,15], in which the control parameters are adjusted between successive iterations, and the so-called composite energy function (CEF) [16] is usually constructed to derive the stability conclusions

Summary

Introduction

Many engineering systems carry out repetitive tasks in fixed finite space, such as manipulators [1,2,3]. In [41], an adaptive learning control design was developed for a certain class of first-order nonlinearly parameterized systems with unknown periodically timevarying delay and further extended to a class of highorder systems with both time-varying and time-invariant parameters. They all required the identical initial conditions on the initial states and the reference trajectory for the AILC design, which is necessary for the stability and convergence analysis but can hardly be satisfied in practical systems. We present a novel AILC scheme for a class of nonlinear time-varying systems with unknown timevarying delays and unknown input dead-zone.

Problem Formulation and Preliminaries

AILC Design

Stability and Convergence Analysis

Simulation Studies

Conclusions