Linear-based gain-determining method for adaptive backstepping controller
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Updated: Oct 21, 2025

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Published on: March 10, 2011
Zhengqi Wang1, Xiaoping Liu1, Wilson Wang2
1Department of Electrical and Computer Engineering, Lakehead University, 955 Oliver Rd, Thunder Bay, Ontario, Canada, P7B 5E1.
Abstract:
This paper presents a linear-based gain-determining method for nonlinear adaptive backstepping controllers. Usually, the gains for nonlinear controllers are tuned by the trial and error method. This method becomes more difficult as the number of gains increases. A user-friendly method is proposed in this work to deal with the problem. Firstly, a linear auxiliary system is formed by separating the linear parts from the nonlinear system. Then, linear state-space techniques are used to determine the gains for state-feedback by the linear auxiliary system. After that, by converting the state-feedback gains to backstepping gains, the gains of the nonlinear backstepping controller can be determined. The proficiency of the gain-determining method is proved by simulations with two linear techniques.
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