Optimal sliding mode control for underactuated systems

This paper introduces a novel method based on nonlinear predictive control to design optimal linear surfaces for sliding model control of underactuated nonlinear systems. The time-invariant parameters of the linear first-order surfaces are selected to achieve some optimal performance objective, such as minimum time or minimum energy. The selection of these surface parameters are subject to constraints that arise from the stability conditions imposed by the sliding mode control law and the physical limits on the system such as control input saturation. The procedure is demonstrated using the inverted pendulum on a cart as an illustrative example.