Fixed-time stabilization control of underactuated bridge crane system

A bridge crane system is an underactuated mechanical system with two degrees of freedom (DOF) and one control input. In this paper, the fixed-time stabilization control problem for this 2-DOF underactuated is studied. First, we approximately linearize the system around the origin based on the system’s actual control objective. And then, a coordinate transformation is constructed to change the linearized system to be a chain system. After that, we construct a sliding mode surface for the chain system and design a controller that drives the system to reach the sliding mode surface within a fixed time. This enables the fixed-time stabilization control objective of the bridge crane system to be achieved. Finally, the numerical simulation results verify the effectiveness of our developed control method.