Incremental Sliding Mode Controller for Large-Scale Underactuated Syetem

An incremental sliding mode controller (ISMC) for a class of large-scale underactutated system is proposed to achieve asymptotic stability and favorable decoupled performance. The large-scale underactuated system includes several subsystems. Firstly, two state variables of a subsystem are chosen to construct the first-layer sliding surface. Secondly, the first-layer sliding surface and one of the left state variables are used to construct the second-layer sliding surface. This process continues till the last sliding surface is constructed. By theoretical analysis, the incremental sliding-mode controller is proved to be globally stable in the sense that all signals involved are bounded, and all system state variables are stable in definite time and will converge to anticipant state. A double inverted pendulum is simulated to demonstrate the validity of this method.