Stochastic boundary control design for extensible marine risers in three dimensional space

This paper presents a new design of boundary controllers for global practical K∞-exponential p-stabilization of vibration motions of extensible marine risers in three-dimensional (3D) space under both stochastic and deterministic sea loads. The control design and analysis of well-posedness and stability of the closed-loop system are carried out based on a new Lyapunov-type theorem, which is developed for studying well-posedness and p-stability of a class of stochastic evolution systems (SESs) in Hilbert space. Since this theorem eases difficulties in verification of the coercivity condition but requires conditions of a form similar to Lyapunov-type theorems for stochastic lumped-parameter systems, it has a potential application to other stochastic distributed-parameter systems.