Boundary control of transverse motion of flexible marine risers under stochastic loads

Abstract

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A constructive design of boundary controllers is proposed to stabilize transverse motion of flexible marine risers under stochastic loads induced by restoring membrane and fluid/air velocity. For stability analysis and boundary control design, global well-posedness (existence and uniqueness) and global stability criteria are developed for nonlinear stochastic evolution systems in Hilbert space subject to both state-dependent and additive stochastic disturbances. These criteria are obtained by developing Lyapunov sufficient conditions from local well-posedness and stability results. The well-posedness and stability developments are not only applied to ensure well-posedness and almost sure (practical) stability of the variational (strong) solution of the stochastic riser system but also to other hyperbolic systems.