Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties |
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| Authors: | Qiao Zhu Jian‐Xin Xu Shiping Yang Guang‐Da Hu |
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| Affiliation: | 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Department of Electrical and Computer Engineering, National University of Singapore 117576, Singapore |
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| Abstract: | This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | repetitive learning control adaptive control backstepping nonlinear discrete‐time systems periodic uncertainties |
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