Adaptive stabilisation of a flexible riser by using the Lyapunov-based barrier backstepping technique

The focuses of this study are the vibration control and constraint problems of an input and output constrained flexible marine riser system, in which system parametric uncertainties are taken into account. Through the combination of integral-barrier Lyapunov function (IBLF), backstepping technique and adaptive technique, an adaptive Lyapunov-based barrier control with an auxiliary system is developed aiming at achieving the control purposes of vibration suppression and constraint satisfaction, where the auxiliary system is to compensate for the input saturation, IBLF is to solve the output constraint and adaptive laws are to handle the parametric uncertainties. In addition, disturbance observer is designed in the barrier term of IBLF, which could attenuate the effects of unknown boundary disturbance. With the proposed control, the uniform boundedness and stability of the closed-loop system are easily achieved. Finally, the significance of the proposed control is demonstrated via numerical simulation.