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Time-varying Barrier Lyapunov Function Based Adaptive Neural Controller Design for Nonlinear Pure-feedback Systems with Unknown Hysteresis

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Abstract

This paper deals with the adaptive neural network (NN) control problem for a class of pure-feedback systems with time-varying constrained states and unknown backlash-like hysteresis. First of all, the considered plant is transferred into a strict feedback system on account of the implicit function theorem and mean value theorem. Then, the time-varying Barrier Lyapunov functions (BLFs) are integrated into the backstepping techniques so that all the states do not transgress the corresponding constraint boundary. This approach avoids the procedure of finding inverse, and therefore greatly improves the robustness of controller. At the same time, the radial basis function (RBF) NNs are employed to identify the unknown internal dynamics, which is a key operation in each step. Based on the Lyapunov stability analysis scheme, all the closed-loop signals are proved to be uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are developed to further verify the proposed control strategy.

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Author information

Authors and Affiliations

  1. College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

    Li Tang

  2. School of Chemical and Environmental Engineering, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

    Dongjuan Li

Authors
  1. Li Tang
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  2. Dongjuan Li
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Corresponding author

Correspondence to Dongjuan Li.

Additional information

Recommended by Editor Hamid Reza Karimi. This work is supported in part by the National Natural Science Foundation of China under Grants 61803190, 61622303, 61603164, 61773188, 61803189, in part by the Program for Liaoning Innovative Research Team in University under Grant LT2016006, in part by the Fundamental Research Funds for the Universities of Liaoning Province under Grant JZL201715402.

Li Tang received the B.S. degree in information and computing science and the M.S. degree in applied mathematics from the Liaoning University of Technology, Jinzhou, China, in 2010 and 2014, respectively. She received the Ph.D. degree with the College of Information Science and Engineering, Northeastern University, Shenyang, China, in 2018. She is currently a Lecturer with the Liaoning University of Technology, Jinzhou. Her current research interests include switched systems, constrained systems and neural-network-based adaptive control.

Dongjuan Li received the B.S. degree in Applied Chemistry from Shenyang University of Technology, China, in 2003. She received the M. S. degree in Chemical Engineering Technology from Dalian Polytechnic University, in 2007. She is currently an Associate Professor with Chemical and Environmental Engineering, Liaoning University of Technology. Her research interests include process control, adaptive control, nonlinear control, neural network control.

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Tang, L., Li, D. Time-varying Barrier Lyapunov Function Based Adaptive Neural Controller Design for Nonlinear Pure-feedback Systems with Unknown Hysteresis. Int. J. Control Autom. Syst. 17, 1642–1654 (2019). https://doi.org/10.1007/s12555-018-0745-y

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  • DOI: https://doi.org/10.1007/s12555-018-0745-y

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