Stabilization control of a flexible marine riser with failed and bounded actuator and time‐varying boundary constraints - Han, Zhiji; Liu, Zhijie; He, Xiuyu (International journal of robust and nonlinear control, 2021)
In this article, we investigate the stabilization control problem of a flexible marine riser system with a failed and bounded control action and time‐varying boundary constraints. The considered system is modeled as a distributed parameter system dominated by a partial differential equation. The involved problems are extended to some more general conditions. The saturation and failures of the actuator make the input and output of the actuator a nonlinear relationship, which leads to the normally designed control input invalid. By applying the Nussbaum gain technique, we report a synthetical control method to tackle the input nonlinearity. A piecewise barrier Lyapunov function (BLF) is introduced to reduce the boundary displacement in an asymmetric open set. Compared with the traditional BLFs, the initial boundary displacement is not forced to retain within the given region by integrating a shifting function into the BLF design. In addition, the adaptive method is combined with the hyperbolic tangent function to provide a smooth control solution to the unknown parameters from nonlinear input and external perturbation. Relying on a Lyapunov‐based analysis and a numerical simulation, it is proven that the actuated riser system is uniformly bounded and the boundary displacement always keeps in the limited set even subject to actuator failures and limitations.