This paper establishes a sector stabilization criterion for a nonlinear flexible marine riser system that incorporates lateral and transverse coupling vibrations, derived from Hamilton's principle. This criterion, grounded in the sector-bounded condition, encompasses a wide range of linear and nonlinear feedback control laws applied to the transverse and lateral directions at the top boundary of the flexible marine riser, respectively. In the analysis, the nonlinear semigroup theory is utilized to establish the well-posedness of the resulting closed-loop coupled system. Notably, the solution demonstrates continuous dependence on the initial conditions. Furthermore, the exponential stability of the closed-loop coupled system is achieved by employing a generalized Gronwall-type integral inequality and the integral multiplier method, which involves the innovative development of an energy-like functional. To demonstrate the effectiveness of the proposed controls, numerical simulations utilizing the finite element method are presented. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Publication:

AUTOMATICA

http://dx.doi.org/10.1016/j.automatica.2025.112618

Author:

Yi Cheng

School of Mathematical Sciences, Bohai University, Jinzhou, 121013, China

Institute of Ocean Research, Bohai University, Jinzhou, 121013, China

E-mail addresses: chengyi407@bhu.edu.cn

Xin Wang

School of Mathematical Sciences, Bohai University, Jinzhou, 121013, China

E-mail addresses: xinw0316@outlook.com

Yuhu Wu

Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, and School of Control Science andEngineering, Dalian University of Technology, Dalian, 116024, China

Corresponding author.

E-mail addresses: wuyuhu@dlut.edu.cn

Bao-Zhu Guo

School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Key Laboratory of System and Control, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China

E-mail addresses: bzguo@iss.ac.cn