This paper deals with, in the framework of absolute stability, boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls. The nonlinear boundary control that satisfies a slope-sector condition covering many types of nonlinear control schemes is a negative feedback of the transverse velocity at the right eyelet of the moving beam. Under the nonlinear control scheme, the well-posedness of the nonlinear partial differential equation which depends continuously on the initial value is investigated by means of the Faedo-Galerkin approximation and priori estimates. By exploiting the integral-type multiplier method, the exponential stability of the closed-loop system is established, where a novel energy like function is constructed. The numerical simulation examples using the finite element method are presented to illustrate the effectiveness of the established criterion of the controller. 

　　Publication: 

　　IEEE Transactions on Automatic Control, 2022, Volume 67, Issue 11, pp: 5714-5729. 

　　Author: 

　　Yi Cheng 

　　School of Mathematical Sciences, Bohai University, Jinzhou, China 

　　Yuhu Wu 

　　Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, and School of Control Science and Engineering, Dalian University of Technology, Dalian, China 

　　Baozhu Guo 

　　School of Mathematics and Physics, North China Electric Power University, Beijing, China 

　　Academy of Mathematics and Systems Science, Academia Sinica, Beijing, China 

　　Email: bzguo@iss.ac.cn