This paper is devoted to establishing global Carleman estimates for refined stochastic beam equations. First, by establishing a fundamental weighted identity, two Carleman estimates are derived with different weight functions for the refined stochastic beam equation, which is a coupled system consisting of a stochastic ordinary differential equation and a stochastic partial differential equation. As applications of these Carleman estimates, the exact controllability of the refined system is proved by the least controls in some sense. Different from classical stochastic beam equations, the refined one is exactly controllable at any time. Meanwhile, the uniqueness of an inverse source problem for refined stochastic beam equations is obtained without any requirement on the initial and terminal data. 

　　Publication: 

　　SIAM Journal on Control and Optimization, Vol. 60, Iss. 5(2022), 10.1137/21M1463513 

　　Author: 

　　Yongyi Yu 

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　Ji-Feng Zhang 

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　School of Mathematics Sciences, University of Chinese Academy of Sciences, Beijing 100149, China 

　　Email: jif@iss.ac.cn