Robust fixed-time stabilization control for underactuated cart-pendulum system

An underactuated cart-pendulum system has two degrees of freedom (DOF) and only one control input. This paper discuss the robust stabilization control of this system around the origin equilibrium point. Firstly, we approximately linearize the system at the origin and change it to be a chained form system. And then, a sliding mode surface is constructed for the system. And we use the sliding mode control method to design a controller that makes the state variables reach the zero sliding mode surface in a fixed time. After that, the stability analysis of closed-loop control system gives that the system is robustly stabilized to the origin in a fixed time. Numerical examples demonstrate the validity of our developed control strategy.