Finite time control of nonlinear underactuated systems using terminal sliding surface

In this paper, we propose a hierarchical terminal sliding mode control approach for nonlinear underactuated systems which can drive the error to zero in a finite time. Here, the controller has the double layer structure because the system is divided into two hierarchical subsystems. In the first layer, the terminal sliding surfaces are hierarchically designed for each subsystem, and in the second layer, the whole sliding surface is designed as the linear combination of terminal sliding surfaces. The asymptotic stability of the system is verified by Lyapunov analysis because the controller is based on terminal sliding surface. Finally, we carry out simulation on a representative underactuated systems such as the overhead crane system, to illustrate the effectiveness of the proposed control scheme.