This paper presents an optimal sliding mode cascade control for stabilization of a class of underactuated nonlinear mechanical systems. A discrete-time, nonlinear model predictive control structure is used to optimally select and update the parameters of the sliding mode control surfaces at specified intervals in order to achieve a desired performance objective. The determination of these surface parameters is 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 input saturation. Nominal stability of the optimal cascade control structure is demonstrated and its robust performance is illustrated using an experimental rotary inverted pendulum system.

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