Adaptive Backstepping Sliding Mode Control of Tractor-trailer System with Input Delay Based on RBF Neural Network
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Adaptive Backstepping Sliding Mode Control of Tractor-trailer System with Input Delay Based on RBF Neural Network Zengke Jin, Zhenying Liang*, Xi Wang, and Mingwen Zheng Abstract: In this paper, an adaptive sliding mode neural network(NN) control method is investigated for input delay tractor-trailer system with two degrees of freedom. An uncertain camera-object kinematic tracking error model of a tractor car with n trailers with input delay is proposed. Radial basis function neural networks(RBFNNs) are applied to approximate the unknown functions in the error model. A sliding mode surface with variable structure control is designed by using backstepping method. Then, an adaptive NN sliding mode control method is thus obtained by combining Lyapunov-Krasovskii functionals. The controller realizes the global asymptotic trajectories tracking of the kinematics system. The stability of the closed-loop system is strictly proved by the Lyapunov theory. Matlab simulation results demonstrate the feasibility of the proposed method. Keywords: Input delay, RBF Neural Network, sliding mode, tracking control, trailers.
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INTRODUCTION
In recent decades, remarkable progress has been made in the control of nonholonomic mobile robot. As the development of research, several promising control methods are proposed, including adaptive, backstepping, sliding mode and so on. Backstepping has gradually become one of the most effective control methods for nonholonomic robot system. It provides a systematic procedure for constructing Lyapunov function [1], and has the ability to restrain the uncertainty and weaken the interference [2]. Sliding mode control has the characteristics of fastresponse, good transient performance, resistance to external disturbances, and robustness to plant parameter variations [3–6]. The controller can effectively eliminate external disturbances when the appropriate sliding mode surface is determined. Due to these characteristics, there are more and more literatures on the backstepping combined with sliding mode control [7, 8]. However, when there are some unknown terms in the systems, it is not easy to solve the problems only by sliding mode control. NN has been regarded as a promising tool in the field of control of nonlinear systems, and has obvious advantages in solving control problems. This is beacuse it has been employed to estimate the uncertain continuous function owing to their inherent approximation capabilities, and relaxing the linear assumption of uncertain parameters [9]. With the help of NN as adaptive control and
function approximator, many NN adaptive controllers are proposed [10]. However, the approximation rate of NN has a directly impact on the response speed of the controlled system. In order to take advantage of NN and sliding mode, some NN sliding model control schemes are proposed [11, 12]. Time delay is often the main cause of systems instability and poor performance, and are often encountered in various physical and engin
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