Adaptive sliding mode controller for a class of second-order underactuated systems

An adaptive hierarchical sliding-mode control (AHSMC) strategy for a class of second-order underactuated systems is presented. First, the whole system is divided into two subsystems. A first-level sliding surface is defined for each subsystem. Then a second-level sliding surface is defined for these two-level sliding surfaces. The AHSMC law is derived in Lyapunov sense when the uncertainties are bounded by an unknown constant. Therefore, the whole system can be drive to its sliding surface and stable. Finally the simulation results show the validity of the proposed method.