Stochastic stabilization of slender beams in space: Modeling and boundary control

Abstract

This paper considers the problem of modeling and boundary feedback stabilization of extensible and shearable slender beams with large deformations and large rotations in space under both deterministic and stochastic loads induced by flows. Fully nonlinear equations of motion of the beams are first derived. Boundary feedback controllers are then designed for global practical exponential p-stabilization of the beams based on the Lyapunov direct method. A new Lyapunov-type theorem is developed to study well-posedness and stability of stochastic evolution systems (SESs) in Hilbert space.